LCM Questions

LCM Questions are given here, along with detailed solutions and proper explanations to help out students regarding the concept of LCM. These questions on LCM will help the students to be able to solve the problems efficiently. Learn more about What is LCM?

The LCM or Lowest Common Multiple of two or more numbers is the least among all the common multiples of given numbers. For example, LCM of 2, 4 and 5 is 20, which is the lowest common multiple of 2, 4 and 5, or we can say 20 is the lowest number which 2, 4 and 5 can divide.

LCM Questions with Solutions

1. If HCF(252, 594) = 18, find LCM(252, 594).

Solution: We have LCM of two numbers = (Product of two numbers)/ their HCF

= (252 × 594)/18 = 8316.

Hence, LCM(252, 594) = 8316

2. Player 1 and player 2 are running around a circular field. Player 1 takes 16 minutes to take one round, while Player 2 completes the round in 20 minutes. If both start simultaneously and go in the same direction, after how much time will they meet at the starting point?

Solution: Time taken by the players to meet again = LCM(16, 20)

Now 16 = 2 4 and 20 = 2 2 × 5

Therefore, LCM(16, 20) = 2 4 × 4 = 80

Hence, both will meet at the starting point after 80 minutes.

3. Is it possible to have two numbers whose HCF is 18 and LCM is 540?

Solution: Since HCF always divides LCM, we see that 540 is divisible by 18, 540/18 = 30.

Thus, it is possible to have two numbers.

4. Find the least number divided by 28 and 32, leaving the remainder 8 and 12, respectively.

Solution: Since 28 – 8 = 20 and 32 – 12 = 20

So we need LCM{(28, 32) – 20} = 224 – 20 = 204

Thus, 204 is required number.

5. Find the least number, which, when divided by 35, 56 and 91, leaves the same remainder of 7, respectively.

Solution: Let us find LCM(35, 56, 91) + 7

56 = 2 × 2 × 2 × 7

91 = 7 × 13

Thus, LCM(35, 56, 91) = 2 3 × 5 × 7 × 13 = 3640

The required number = LCM(35, 56, 91) + 7 = 3640 + 7 = 3647.

6. Two alarm clocks ring their alarms at regular intervals of 72 seconds and 50 seconds. If they beep together at noon, at what time will they beep again for the first time?

Solution: We find the LCM of 72 and 50.

Prime factorisation of 72 and 50,

72 = 2 × 2 × 2 × 3 × 3

50 = 2 × 5 × 5

Therefore, the LCM of 72 and 50 = 2 3 × 3 2 × 5 2 = 1800

1800 seconds = 1800/60 min = 30 min

Hence, the clocks will beep again for the first time at 12:30 pm.

7. There are 56 students in section A and 58 students in section B of a class in a school. Find the minimum number of books required for their class library so that they can be distributed equally among the students of section A or section B.

Solution: Clearly, the number of books that are to be equally distributed should be multiple of 56 and of 58. Thus, we have to find LCM of 56 and 58.

Now, 56 = 2 × 2 × 2 × 7

58 = 2 × 29

LCM (56, 58) = 2 3 × 7 × 29 = 1624.

Hence, atleast 1624 books are required in the library.

  • Euclid’s Division Lemma
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8. Find the LCM of 96(x – 1)(x + 1) 2 (x + 3) 3 and 64(x 2 – 1)(x + 3)(x + 2) 2 .

Solution: Let f(x) = 96(x – 1)(x + 1) 2 (x + 3) 3

And g(x) = 64(x 2 – 1)(x + 3)(x + 2) 2

Now, factorising the polynomials into irreducible factors.

f(x) = 2 × 2 × 2 × 2 × 2 × 3 × (x – 1)(x + 1) 2 (x + 3) 3

g(x) = 2 × 2 × 2 × 2 × 2 × 2 × (x + 1)(x – 1)(x + 3)(x + 2) 2

Taking all the factors raised to their highest exponents: 2 6 , 3, (x – 1), (x + 1) 2 , (x + 3) 3 , (x + 2) 2

⇒ The LCM of the given polynomials = 192(x – 1)(x + 1) 2 (x + 2) 2 (x + 3) 3 .

9. Find the LCM of ⅔, ¾ and 7/2.

Solution: LCM of ⅔, ¾ and 7/2 = [LCM of (2, 3, 7)]/[HCF of (3, 4, 2)]

LCM of (2, 3, 7) = 2 × 3 × 7 = 42

HCF of (3, 4, 2) = 1

Therefore, LCM of ⅔, ¾ and 7/2 = 42.

10. Find the LCM of 22.5, 3.5 and 0.55.

Solution: Converting the decimals into integers,

22.5 = 22.5 × 100 = 2250

3.5 = 3.5 × 100 = 350

0.55 × 100 = 55

Now, 2250 = 2 × 3 × 3 × 5 × 5 × 5

350 = 2 × 5 × 5 × 7

55 = 5 × 11

LCM (225, 350, 55) = 2 × 3 2 × 5 3 × 7 × 11 = 173250

Place a decimal point after place from right

Then, LCM(22.5, 3.5, 0.55) = 1732.5.

11. Find the smallest number, which is, when reduced by 7, is divisible by 12, 16, 18, 21 and 28.

Solution: Let x be a number when reduced by 7, is divisible by 12, 16, 18, 21 and 28.

Then, x – 7 = m × 12 ⇒ x = m × 12 + 7.

Thus, when x is divided by 12, it leaves a remainder of 7, which is the same for each given number.

∴ x = LCM (12, 16, 18, 21, 28) + 7 = 1008 + 7 = 1015.

12. Find the largest four-digit number, which is divided by 4, 7 and 13, leaving a remainder of 3, respectively.

Solution: Largest 4-digit number = 9999

LCM (4, 7, 13) = 364

Now 9999 = 27 × 364 + 171

Thus, the 4-digit number divisible by 4, 7 and 13 = 9999 – 171 = 9828.

Since the number we have to find leaves a remainder of three when divided by 4, 7 and 13,

∴ 9828 + 3 = 9831 is the required number.

13. Six bells commence tolling together. After that, they toll at a time interval of 2, 4, 6, 8, 10 and 12 seconds, respectively. In 60 minutes, how many times do they toll together?

Solution: Taking LCM (2, 4, 6, 8, 10, 12) = 120

So, the bells will toll together after each 120 seconds = 2 min

∴ In 60 minutes number of times the bells will toll = 60/2 + 1 = 31 times.

Video Lesson on Application of LCM

solving word problem involving lcm

Related Articles:

Practice questions:.

1. If the LCM of 12x 3 y 2 and 18x p y 3 is 36x 4 y 3 . Find the value of p.

2. The sum of LCM and HCF of the two numbers is 1260. If their LCM is 900 more than their HCF, find the product of two numbers.

3. The LCM and HCF of two numbers are equal; the numbers must be ______.

4. Two bells toll at an interval of 24 minutes and 36 minutes, respectively. If they tolled together at 9 am, after how many minutes do they toll together again, at the earliest?

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Word Problems on L.C.M.

Let us consider some of the word problems on l.c.m. (least common multiple).

1.  Find the lowest number which is exactly divisible by 18 and 24.

We find the L.C.M. of 18 and 24 to get the required number.

LCM Problems

L.C.M. = 2 × 3 × 3 × 4 = 72

Therefore, 72 is the required number.

2.  Find the lowest number which is less by 5 to be divided by 16, 24 and 36 exactly.

We find the L.C.M. of 16, 24 and 36.

Word Problems on L.C.M.

L.C.M. = 2 × 2 × 2 × 3 × 2 × 3 = 144

Now subtract 5 from 144 to get the required number.

144 - 5 = 139

Therefore, 139 is the required number.

3. Find the lowest number which is more by 6 to be divided by 25, 40 and 60 exactly.

We find the L.C.M. of 25, 40 and 60.

L.C.M. of 25, 40 and 60

L.C.M. = 2 × 2 × 5 × 5 × 2 × 3 = 600

Therefore, the required number is 600 + 6 = 606.

4.  A shopkeeper sells candles in packets of 12 and candle stands in packet of 8. What is the least number of candles and candle stands Nita should buy so that there will be one candle for each candle stand.

To find a quantity which is the lowest common multiple of different quantities, we find the LCM.

Multiples of 12 are 12, 24, 36, 48, ……

Multiples of 8 are 8, 16, 24, 32, 40, ……

The lowest common multiple is 24. So, the least number of candles and candle stand that Nita should buy is 24.

Word Problems on L.C.M.

5.  Find the lowest number which leaves 3 as remainder when divided by 8, 12 and 16.

We find the L.C.M. of 8, 12 and 16.

Find the Lowest Number

L.C.M. = 2 × 2 × 2 × 3 × 2 = 48

If we add 3 to 48 it becomes 51 which leaves 3 as remainder when divided by 8, 12 and 16.

Therefore, the required number is 48 + 3 = 51.

6. A florist wants to arrange 24 boquets of flowers in different rows. Find out in how many ways he can arrange the bouquets with same number in each row.

We need to find all the factors of 24.

24 = 1 × 24, 24 = 2 × 12, 24 = 3 × 8, 24 = 4 × 6

The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24

He can arrange rows of 1, 2, 3, 4, 6, 8, 12 and 24 boquets.

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GCF and LCM word problems

Factors and multiples.

These word problems need the use of greatest common factors (GCFs) or least common multiples (LCMs) to solve. Mixing GCF and LCM word problems encourages students to read and think about the questions, rather than simply recognizing a pattern to the solutions.

solving word problem involving lcm

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Word Problems that uses GCF or LCM (Worksheets)

Related Topics & Worksheets: Least Common Multiple More Math Worksheets

Objective: I can find the least common multiple or least common denominator.

Read the lesson on least common multiple if you need to learn how to find the lowest common multiple.

We use the least common multiple when adding or subtracting fractions with unlike denominators. It is then called the least common denominator.

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Least common multiple word problems

Eight interesting and fun least common multiple word problems you can give to your students to tease them. If your students can solve these problems, they can probably solve any word problems about the least common multiple.

Word problem #1 Today, both the soccer team and the basketball team had games. The soccer team plays every 3 days and the basketball team plays every 5 days. When will both teams have games on the same day again?

Word problem #2

A manager at a restaurant can buy hamburger buns in packages of 8 and hamburger patties in packages of 6. Suppose that the manager cannot buy part of a package. What is the least number of packages of each product he can buy to have an equal number of hamburger patties and buns? 

Word problem #3

A man smiles at his beautiful wife every 3 seconds while the wife smiles back at him every 6 seconds. When will both husband and wife smile at each other at the same time?

Word problem #4

Steve can save 9 dollars every day while Maria can save 12 dollars every day. What is the least number of days it will take each person to save the same amount of money?

More Interesting and fun least common multiple word problems

Boxes that are 12 inches tall are being piled next to boxes that are 10 inches tall. What is the least height in feet at which the two piles will be the same height? Word problem #6 A radio station plays "yesterday" by the Beatles once every 2 days. Another radio station plays the same song once every 3 days. How many times in 30 days will both radio stations play the same song on the same day?

Word problem #7 Two men running a marathon took a sip of water at the same time 72 minutes after they started the race. If the first man took a sip of water every 9 minutes, how often did the other man take a sip of water? Word problem #8 A train to New York city leaves a station every 7 minutes. Another train to Boston leaves the station every 6 minutes. Suppose it is 6:30 am right now. At what time will both trains leave the station together?

A least common multiple word problem about barking dogs

Five dogs in a neighborhood were barking consistently last night. The names of the dogs are Lucy, Max, Murphy, Daisy, and Sam. The dogs started barking at 10 P.M. Then, Lucy barked every 5 minutes, Max barked every 3 minutes, Murphy barked every 4 minutes, Daisy barked every 3 minutes, and Sam barked every minute. Why did Mr. Smith suddenly awaken at 11 P.M.?

What is the least common multiple

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Word Problems on H.C.F. and L.C.M | HCF and LCM Problems with Solutions

Get an idea on how to Solve Word Problems on Highest Common Factor and Least Common Multiple. Try to answer the LCM and HCF Questions available here on your own and then verify with ours. Read the Question Carefully and understand what is asked so that you won’t have any difficulty in solving the LCM and HCF Word Problems. Learn the tips & tricks to solve Highest Common Factor and Least Common Multiple Problems easily and answer the questions you come across in your exams with utmost confidence.

Also, Check:

  • Worksheet on H.C.F. and L.C.M
  • Relationship between H.C.F. and L.C.M
  • Worksheet on Methods of H.C.F.and L.C.M.

Word Problems Involving H.C.F and L.C.M

Example 1. Find the multiple of 40 which is in between 400 and 500 where the digits at tens place and hundreds place are equal? Solution: Multiples of 40 are 40,80,120,160,200,240,280,320,360,400,440,480,520 etc. Given the number is in between 400 and 500 Here the numbers between 400 and 500 are 400,440,480. Also given the digits at tens place and hundreds place are equal. Here 440 is the number which has the same digit at tens place and hundreds place are equal.

Example 2. Vijay’s friend asked him to bring the same number of chocolates and biscuits. The store sells chocolates in packs of 50, biscuits in packs of 20. Find how many chocolates Vijay will buy from the store? Solution: The store sells chocolates in packs of 50, biscuits in packs of 20. Vijay has to buy the same number of chocolates and biscuits. Now we have to find the LCM of Chocolates and Biscuits. i.e. LCM(50,20) 50=2 × 5× 5 =2 ×  5 2 20=2 × 2 ×  5=2 2 × 5 LCM(50,20)=2 2 × 5 2 =4 × 5=20

Example 3. Find the least number of square tiles by which the floor of a room of dimensions 1223 cm, 634 cm can be covered completely? Solution: We require the least number of square tiles, so each tile must be of maximum dimension. To get the maximum dimension of tile, we have to find the largest number that exactly divides 1873 cm,958 cm. HCF(1223, 634)=1 cm Hence, the side of a square tile is 1 cm. Required no. of tiles= Area of the floor/Area of a square tile =1223.634/1.1 =775382

Example 4. Anjali goes to dancing classes every 5th day. Sandhya goes to the same dance class every 4  th day. How many days will they meet in the dance class in the month of July and august if we start counting from 1st July? Solution: Given, Anjali goes to dancing classes every 5th day. Sandhya goes to the same dance class every 4 th day. Then from starting the first day, the number of days when they meet=LCM(5,6)=30 So every 20 th day they will meet. They will meet only once on July 20.

Practice Math Online with Unlimited Questions provided in 5th Grade Math Activity Sheets and become a blossoming mathematician in no time.

Example 5. A certain no. of fruits are stored in groups of 2,4,6,8 with no fruit left behind. Find the no. of fruits? Solution: Given, Fruits are stored in groups of 2,4,6,8. No. of fruits=LCM(2,4,6,8) =24 fruits Hence, there are 24 fruits.

Example 6. Sameera can jump 5 steps at a time and Nilima can jump 6 steps at a time. On which of the steps will both meet if both start jumping together? Solution: Given, Sameera can jump  at a time= 5 steps Nilima can jump at a time= 6 steps if both starts jumping together, they will meet=LCM(5,6) =30

Example 7. Satvika has music classes on alternate days, dance class once in 4 days, and yoga class once on 4 days. On the 1st of Dec, she had all the 3 classes. When will she have all the 3classes again? Solution: Given, Satvika has music classes on alternate days i.e. every second day. dance classes =4 days, yoga classes=3 days Satvika will have all the 3 classes =LCM(2,4,3) =12 Hence, Satvika will have all three classes on 13th December.

hcf example

Example 9. Find the least number of plants in a group such that they are planted in the rows of 5,10,15? Solution: To find the least number of plants first we have to find the LCM of(5,10,15). LCM(5,10,15)=30 So we need 30 plants to be planted in rows of 5,10,15.

HCF example 2

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LEAST COMMON MULTIPLE WORD PROBLEMS

Problem 1 :

Omar is planting trees. He  has enough trees to plant 6, 7, or 14  trees in each row. What is the least  number of trees Omar could have ?

Solution : 

To find the least number of trees, we have to find the least number that is evenly divisible by 6, 7 and 14. That is the least common multiple of 6, 7 and 14.

Find the least common multiple of 6, 7 and 14.

solving word problem involving lcm

LCM  =  Product of all prime factors

=  7  ⋅ 2   ⋅  3

The least number of trees required to plant 6, 7 or 14 tress in each row is 42. 

Problem 2 :

The Line A bus arrives at the  bus stop every 25 minutes, and the  Line B bus arrives every 15 minutes.  They are both at the bus stop right  now. In how many minutes will they  both be at the bus stop again ?

For example, let the two buses arrive at the bus stop after every 3 minutes  and 4 minutes. 

Then the Line A bus arrives after 3, 6, 9, 12 minutes...... 

Like this, the Line B  bus arrives after 4, 8, 12, 16 minutes...... 

If both the buses arrive now, again they will arrive together after 12 minutes. This 12 is the least common multiple (LCM) of 3 and 4.  

The same thing happened in our problem. To find the time, when both the buses are at the bus stop again, we have to find the LCM of (25, 15). 

LCM (25, 15)  =  75

75 minutes  =  1 hour 15 minutes

So, both the buses will be at the bus stop again in 1 hour 15 minutes. 

Problem 3 :

The high school  marching band rehearses with either  6 or 10 members in every line. What is  the least number of people that can be  in the marching band ?

To find the least number of people, we have to find the least number that is evenly divisible by 6 and 10. That is the least common multiple of 6 and 10.

LCM (6, 10)  =  30

The least number of people i n the marching band is 30. 

Problem 4 :

Two numbers are in the ratio 4 : 7. If the second number is 35, find their least common multiple.

Because the two numbers are in the ratio 4 : 7, the numbers can be assumed as 4x and 7x.

But, it is given that the second number is 35.

Then, 

7x  =  35

Divide each side by 7.

x  =  5

The first number  =  4(5)  =  20.   

LCM (20, 35)  =  140

So, the least common multiple of the two numbers is 140

Problem 5 :

Two numbers are in the ratio 2 : 3 and their least common multiple is 84 . Find the numbers. 

Because the two numbers are in the ratio 2 : 3, the numbers can be assumed as 2x and 3x.

Least common multiple (2x, 3x)  =  6x 

But, it is given that the least common multiple of the two numbers is 84.

6x  =  84

Divide each side by 6. 

x  =  14

Substitute x = 8 in 2x and 3x.

2x  =  2(14)  =  28

3x  =  3(14)  =  42

So, the two numbers are 28 and 42.

Problem 6 :

Two numbers are in the ratio 5 : 6 and their sum is 44. Find their least common multiple. 

Because the two numbers are in the ratio 5 : 6, the numbers can be assumed as 5x and 6x.

5x + 6x  =  44

11x  =  44

Divide each side by 11. 

x  =  4

Substitute x = 4 in 5x and 6x. 

5x  =  5(4)  =  20

6x  =  6(4)  =  24

The two numbers are 20 and 24.

LCM (20, 24)  =  120

So, the least common multiple of the two numbers is 120.

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Gcf and Lcm Word Problems Worksheets

GCF and LCM word problems worksheets can help encourage students to read and think about the questions, rather than simply recognizing a pattern to the solutions. GCF and LCM word problems worksheets come with the answer key and detailed solutions which the students can refer to anytime.

Benefits of GCF and LCM Word Problems Worksheets

GCF and LCM word problems worksheets help kids to improve their speed, accuracy, logical and reasoning skills.

GCF and LCM word problems worksheets give students the opportunity to solve a wide variety of problems helping them to build a robust mathematical foundation. GCF and LCM word problems worksheets help kids to improve their speed, accuracy, logical and reasoning skills in performing simple calculations related to the topic of GCF and LCM.

GCF and LCM word problems worksheets are also helpful for students to prepare for various competitive exams.

These worksheets come with visual simulation for students to see the problems in action, and provides a detailed step-by-step solution for students to understand the process better, and a worksheet properly explained about the GCF and LCM.

Download GCF and LCM Word Problems Worksheet PDFs

These math worksheets should be practiced regularly and are free to download in PDF formats.

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  • \mathrm{Lauren's\:age\:is\:half\:of\:Joe's\:age.\:Emma\:is\:four\:years\:older\:than\:Joe.\:The\:sum\:of\:Lauren,\:Emma,\:and\:Joe's\:age\:is\:54.\:How\:old\:is\:Joe?}
  • \mathrm{Kira\:went\:for\:a\:drive\:in\:her\:new\:car.\:She\:drove\:for\:142.5\:miles\:at\:a\:speed\:of\:57\:mph.\:For\:how\:many\:hours\:did\:she\:drive?}
  • \mathrm{The\:sum\:of\:two\:numbers\:is\:249\:.\:Twice\:the\:larger\:number\:plus\:three\:times\:the\:smaller\:number\:is\:591\:.\:Find\:the\:numbers.}
  • \mathrm{If\:2\:tacos\:and\:3\:drinks\:cost\:12\:and\:3\:tacos\:and\:2\:drinks\:cost\:13\:how\:much\:does\:a\:taco\:cost?}
  • \mathrm{You\:deposit\:3000\:in\:an\:account\:earning\:2\%\:interest\:compounded\:monthly.\:How\:much\:will\:you\:have\:in\:the\:account\:in\:15\:years?}
  • How do you solve word problems?
  • To solve word problems start by reading the problem carefully and understanding what it's asking. Try underlining or highlighting key information, such as numbers and key words that indicate what operation is needed to perform. Translate the problem into mathematical expressions or equations, and use the information and equations generated to solve for the answer.
  • How do you identify word problems in math?
  • Word problems in math can be identified by the use of language that describes a situation or scenario. Word problems often use words and phrases which indicate that performing calculations is needed to find a solution. Additionally, word problems will often include specific information such as numbers, measurements, and units that needed to be used to solve the problem.
  • Is there a calculator that can solve word problems?
  • Symbolab is the best calculator for solving a wide range of word problems, including age problems, distance problems, cost problems, investments problems, number problems, and percent problems.
  • What is an age problem?
  • An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

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  • High School Math Solutions – Inequalities Calculator, Exponential Inequalities Last post, we talked about how to solve logarithmic inequalities. This post, we will learn how to solve exponential...

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IMAGES

  1. GCF and LCM Word Problems

    solving word problem involving lcm

  2. LCM Word Problems -1

    solving word problem involving lcm

  3. Solving An LCM Word Problem

    solving word problem involving lcm

  4. GCF and LCM Word Problems Worksheets

    solving word problem involving lcm

  5. Gcf And Lcm Word Problems Worksheet

    solving word problem involving lcm

  6. Gcf And Lcm Word Problems #1

    solving word problem involving lcm

VIDEO

  1. LCM problem solving#maths #mathtricks #subject #trendingshorts #viral

  2. ANGELO AMBAT SOLVING REAL LIFE PROBLEMS INVOLVING GCF AND LCM QUARTER 1, WEEK 4

  3. solving word problems by champs1

  4. Solving a Word Problem Involving Rates and Time Conversion

  5. 101. Solving a word problem involving consecutive integers

  6. SOLVING WORD PROBLEMS IN TRIGONOMETRY

COMMENTS

  1. LCM Questions with Solutions

    LCM Questions are given here, along with detailed solutions and proper explanations to help out students regarding the concept of LCM. These questions on LCM will help the students to be able to solve the problems efficiently. Learn more about What is LCM?. The LCM or Lowest Common Multiple of two or more numbers is the least among all the common multiples of given numbers.

  2. L.C.M. Word Problems

    3. Find the lowest number which is more by 6 to be divided by 25, 40 and 60 exactly. We find the L.C.M. of 25, 40 and 60. L.C.M. = 2 × 2 × 5 × 5 × 2 × 3 = 600. Therefore, the required number is 600 + 6 = 606. 4. A shopkeeper sells candles in packets of 12 and candle stands in packet of 8. What is the least number of candles and candle ...

  3. Word Problems on L.C.M

    LCM Word Problems with Answers. Example 1. Find the lowest number which is exactly divisible by 12, 16. Solution: We have to find the Lcm to find the lowest number exactly divisible by 12,16. LCM= 2 ×2 × 3 × 4=48. Therefore, 48 is the lowest number exactly divisible by 12, 16. Example 2.

  4. GCF and LCM Word Problems

    These word problems need the use of greatest common factors (GCFs) or least common multiples (LCMs) to solve. Mixing GCF and LCM word problems encourages students to read and think about the questions, rather than simply recognizing a pattern to the solutions. Worksheet #1 Worksheet #2 Worksheet #3 Worksheet #4. Worksheet #5 Worksheet #6.

  5. GCF & LCM word problems (video)

    However, for some problems, this method is not always the most efficient method. Efficiency might matter if your test is timed. For example, if one of two numbers is a multiple of the other number, then the LCM of the two numbers is the larger number (for example, because 24 is a multiple of 8, LCM(8,24) is 24).

  6. GCF & LCM word problems (practice)

    Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere. ... GCF & LCM word problems. Greatest common factor review. Math > MAP Recommended Practice > Numbers ...

  7. Solving a LCM word problem

    LCM word problems find the minimum amount or an event that repeatsStandards 6NS. 46.NS.B.4 Find the greatest common factor of two whole numbers less than or ...

  8. Word Problems that uses GCF or LCM (Worksheets)

    Solve the following problems: a) Tim has a bag of 36 orange-flavoured sweets and Peter has a bag of 44 grape-flavoured sweets. They have to divide up the sweets into small trays with equal number of sweets; each tray containing either orange-flavoured or grape-flavoured sweets only. If there is no remainder, find the largest possible number of ...

  9. LCM and GCF word problems

    Courses on Khan Academy are always 100% free. Start practicing—and saving your progress—now: https://www.khanacademy.org/math/mappers/number-and-operations-...

  10. PDF Word Problems Involving Greatest Common Factor And Least Common Multiple

    Word Problems Involving Highest Common Factor and Lowest Common Multiple. Read each question carefully and think about what the question is asking. Find the prime factors for each number Draw a Prime factor diagram. Remember Numbers in the overlap = HCF Numbers in the whole diagram = LCM. 1.

  11. PDF GCF and LCM Word Problems

    GCF and LCM Word Problems Solve each word problem by finding GCF or LCM. 1. Pencils come in packages of 10. Erasers come in packages of 12. Phillip wants ... GCF and LCM Word Problems Answer Key 1. 10 - 10, 20, 30, 40, 50, 60 12 - 12, 24, 36, 48, 60 LCM = 60

  12. Least Common Multiple Word Problems

    A least common multiple word problem about barking dogs. Five dogs in a neighborhood were barking consistently last night. The names of the dogs are Lucy, Max, Murphy, Daisy, and Sam. The dogs started barking at 10 P.M. Then, Lucy barked every 5 minutes, Max barked every 3 minutes, Murphy barked every 4 minutes, Daisy barked every 3 minutes ...

  13. GCF & LCM

    The factors of 18 are: 1, 2, 3, 6, 9 and 18. The common factors of 12 and 18 are 1, 2, 3 and 6. The greatest number in these common factors is 6, hence the GCF of 12 and 18 is 6. LCM of 12 and 18 ...

  14. Using the LCM (Least Common Multiple) to Solve Problems

    Using the LCM to solve the problem directly. The problem tells us that there are the same number of gold coins on each island, but distributed in different ways. On one of the islands, Buck the Buccaneer will find the coins in chests of 8. On the other, Piper the Pirate will find them in chests of 36. We know that if the pirates add their ...

  15. HCF and LCM Problems with Solutions

    Read the Question Carefully and understand what is asked so that you won't have any difficulty in solving the LCM and HCF Word Problems. Learn the tips & tricks to solve Highest Common Factor and Least Common Multiple Problems easily and answer the questions you come across in your exams with utmost confidence. Also, Check: Worksheet on H.C.F ...

  16. PDF Multiples, L.C.M. & Word Problems involving H.C.F. & L.C.M.

    This problem can be solved using H.C.F. Here, we are cutting the ribbon into smaller pieces. As we want to have pieces of equal length, we need to find a number that exactly divides both 18 and 24 (that is, common factors). As we are looking to have pieces of ribbon that are as long as possible, we are looking for the highest common factor.

  17. Least Common Multiple Word Problems

    x = 5. The first number = 4 (5) = 20. LCM (20, 35) = 140. So, the least common multiple of the two numbers is 140. Problem 5 : Two numbers are in the ratio 2 : 3 and their least common multiple is 84. Find the numbers. Solution : Because the two numbers are in the ratio 2 : 3, the numbers can be assumed as 2x and 3x.

  18. Gcf and Lcm Word Problems Worksheets

    These math worksheets should be practiced regularly and are free to download in PDF formats. GCF and LCM Word Problems Worksheet - 1. Download PDF. GCF and LCM Word Problems Worksheet - 2. Download PDF. GCF and LCM Word Problems Worksheet - 3. Download PDF. GCF and LCM Word Problems Worksheet - 4. Download PDF.

  19. GCF and LCM Word Problems

    Clear explanation on how to analyze problem solving involving Greatest Common Factor and Least Common Multiple.

  20. Word Problems Calculator

    An age problem is a type of word problem in math that involves calculating the age of one or more people at a specific point in time. These problems often use phrases such as 'x years ago,' 'in y years,' or 'y years later,' which indicate that the problem is related to time and age.

  21. HCF AND LCM WORD PROBLEMS

    So, each tile must be of maximum dimension. To get the maximum dimension of the tile, we have to find the largest number which exactly divides 16.58 and 8.32. That is nothing but the H.C.F of (16.58, 8.32). To convert meters into centimeters, we have to multiply by 100. 16.58 ⋅ 100 = 1658 cm. 8.32 ⋅ 100 = 832 cm.

  22. Solving GCF and LCM Word Problems for Enhanced Problem-Solving Skills

    To solve word problems involving GCF and LCM, it is important to carefully read the problem, identify the key numbers, list factors or multiples, determine common factors or multiples, and check the solution for accuracy. Avoid common mistakes by clearly understanding the difference between GCF and LCM and considering the units in the problem.

  23. GCSE (9-1) Maths

    GCSE lcm word problems Questions and Answers. Question. Answer. ... Hard. Solve in: min. Use Calculator: No. Tags: Numbers lcm word problems. Question. Answer. These detailed solutions are visible only for premium members. Please register to unlock over 135+ GCSE Maths Solved Past & Predicted Papers. 5,000+ Topicwise Questions with Step by Step ...