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In this lesson, we will learn how to find the least common multiple of two or more numbers and how to use that to solve real-world problems.

Q1:

Find the LCM of 6, 15, and 40.

Q2:

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?

Q3:

What is the least common multiple of 8 and 10?

Q4:

What is the least common multiple of 6 and 10?

Q5:

What is the least common multiple of 4 and 9?

Q6:

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.

Q7:

What is the least common multiple of 6 and 3?

Q8:

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

Q9:

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

Q10:

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.

Q11:

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?

Q12:

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

Q13:

Which of the following describes all of the common multiples of 26 and 30? Note that π is any positive, whole numbers.

Q14:

Karim needs cards and envelopes. The cards are sold in packs of 8 and the envelopes in packs of 12. Find the minimum number of packs of each he needs to buy to have the same number of cards and envelopes.

Q15:

What is the least common multiple of 4 and 10?

Q16:

Can the least common multiple of two numbers be the smaller number?

Q17:

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?

Q18:

Find the least common multiple of 5 and 10.

Q19:

What is the least common multiple of 6 and 2?

Q20:

Find the least common multiple of 8 and 12.

Q21:

Every 3 years, Huntington School hosts the state gymnastics competition. Every 7 years, it hosts the state maths 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?

Q22:

Find the least common multiple of 5 and 12.

Q23:

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?

Q24:

Find the least common multiple of 6 and 9.

Q25:

In an inline speed skating competition, Sherif completes each lap in 20 seconds, Maged completes each lap in 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.

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