Worksheet: The Least Common Multiple

In this worksheet, we will practice finding the least common multiple of two or more numbers and using that to solve real-world problems.

Q1:

Find the LCM of 6, 15, and 40.

Q2:

Find the two numbers whose LCM is 45 and sum is 54.

  • A 18 and 90
  • B 18 and 36
  • C 10 and 47
  • D 9 and 45

Q3:

A quarter moon occurs every 15 days. If the last quarter moon occurred on a Monday, how many days will pass before a quarter moon occurs again on a Monday?

Q4:

Karim is printing green and yellow stickers. He noticed that a page can fit 6 green stickers or 8 yellow ones. If he wants to print the exact same number of green and yellow stickers, what is the least number of green stickers he could print?

Q5:

Every 3 years, Huntington School hosts the state gymnastics competition. Every 7 years, it hosts the state math competition. If the last time the school hosted both events in the same year was in 2003, in what year will the school host both events in the same year again?

  • A2010
  • B2013
  • C2023
  • D2024
  • E2020

Q6:

What is the least common multiple of 4 and 9?

Q7:

What is the least common multiple of 4 and 10?

Q8:

What is the least common multiple of 7 and 5?

Q9:

Find the LCM of 1 , 2 , and 4.

Q10:

List the next five common multiples after the LCM of 2 and 16.

  • A4, 8, 12, 16, 20
  • B16, 32, 48, 64, 80
  • C4, 6, 8, 10, 12
  • D32, 48, 64, 80, 96
  • E32, 64, 96, 128, 160

Q11:

Yara goes to the library every 6 weeks. Farida goes to the same library every 7 weeks. If they met at the library one day, how long would it be before both of them are at the library in the same week again?

Q12:

Write three numbers that have an LCM of 210.

  • A2, 7, 21
  • B5, 15, 21
  • C2, 15, 5
  • D2, 15, 21
  • E2, 5, 7

Q13:

The FIFA world Cup takes place every 4 years, and the US census is taken every 10 years; both took place in 2010. When is the next year in which both events will happen?

  • A2050
  • B2020
  • C2024
  • D2030
  • E2014

Q14:

What is the least common multiple of 8 and 10?

Q15:

What is the least common multiple of 6 and 10?

Q16:

Bassem and Shady are hosting a BBQ party. Bassem is buying hamburgers that come in packs of 9, and Shady is buying buns that come in packs of 6. Given that they want to buy the same number of hamburgers and buns, find the least number of hamburgers they can buy.

Q17:

What is the least common multiple of 6 and 3?

Q18:

Chloe is buying disposable cups and plates for a party. Cups come in packs of 6 and plates in packs of 8. The store does not sell parts of a pack, and Chloe wants to have the same number of cups as plates. What is the smallest total number of cups she can purchase?

Q19:

The LCM of two consecutive positive numbers is greater than 300 and is a multiple of 9. Determine the least possible values of the two numbers.

  • A18, 19
  • B18, 18
  • C17, 19
  • D17, 18

Q20:

Which of the following describes all of the common multiples of 28 and 42? Note that 𝑛 is any positive, whole numbers.

  • A 2 8 𝑛
  • B 1 1 7 6 𝑛
  • C 4 2 𝑛
  • D 8 4 𝑛
  • E 7 0 𝑛

Q21:

What is the least common multiple of 6 and 2?

Q22:

In an inline speed skating competition, Sherif completes each lap in 20 seconds, Maged completes each lap in 1 1 3 minutes, and Adam completes each lap in 30 seconds. Given that they all start skating simultaneously, determine how many minutes will pass before they all cross the start line together again.

  • A 1 4 min
  • B 1 min
  • C 1 1 3 min
  • D 4 min

Q23:

Nada goes to the park every two days, and she goes to the ice cream shop once a week. One day, Nada went to the park and then went to the ice cream shop. How many days will pass before she does both activities on the same day again?

Q24:

Mona and Mariam start running in the park together. It takes Mona 4 minutes and Mariam 6 minutes to run one lap. How long before they are together again at the starting point?

  • A 4 minutes
  • B 6 minutes
  • C 8 minutes
  • D 12 minutes
  • E 18 minutes

Q25:

Is the following statement true or false? The LCM of an odd number and an even number is always even.

  • ATrue
  • BFalse

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