# Worksheet: Finding the Least Common Multiple

Q1:

List the next five common multiples after the LCM of 8 and 14.

• A112, 224, 336, 448, 560
• B4, 6, 8, 10, 12
• C112, 168, 224, 280, 336
• D4, 8, 12, 16, 20
• E56, 112, 168, 224, 280

Q2:

What is the least common multiple of 6 and 3?

Q3:

Find the LCM of 6, 15, and 40.

Q4:

Find the LCM of , and 75.

Q5:

Write three numbers that have an LCM of 308.

• A4, 8, 6
• B4, 11, 8
• C4, 11, 28
• D4, 6, 28
• E8, 11, 28

Q6:

Find the two numbers whose LCM is 96 and sum is 56.

• A25 and 34
• B24 and 32
• C48 and 64
• D42 and 7

Q7:

Find the LCM of two numbers where the prime factors of the first are 2, 2, 3, and 3 and the prime factors of the second are 2, 2, 3, and 17.

• A459
• B612
• C272
• D306

Q8:

A botanist waters one plant every 79 days and another every 17 days. If she waters both plants today, in how many days will she water the two plants on the same day again?

• Aafter 95 days
• Bafter
1 343
days
• Cafter 96 days
• Dafter
1 342
days

Q9:

Peter bought flowers to plant in his garden. He bough the smallest number of flowers that would allow him to choose to plant them in equal rows of either 3, 15, or 25 flowers. How many flowers did he buy?

Q10:

Every 6 years, a group of university graduates organizes their own reunion. Every 9 years, the same university organizes an official reunion for its alumni. If both reunions took place in 2007, in what year will both reunions take place again?

• A2037
• B2061
• C2025
• D2022
• E2019

Q11:

At a school picnic, every child is given a yogurt, an apple, and a brownie. Yogurts come in packets of 6, apples in bags of 5, and brownies in packages of 10. When all the children have been served, they realise that they have used a whole number of packets of yogurt, a whole number of bags of apples, and a whole number of packages of brownies. What is the least number of students there could have been for this to happen?

Q12:

Wayne is putting stock on his store’s shelves. He knows he can lay out the soap by putting 7 or 11 soap bars on each shelf. What is the least number of soap bars Wayne could have at his store?

Q13:

Heather goes to the library every 4 weeks. Nicole goes to the same library every 6 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?

Q14:

A recipe for oatmeal cookies makes 32 cookies, and another recipe for chocolate chip cookies makes 4 dozen cookies. Given that a person wants to have the same number for each type of cookies, determine the least number for each cookie type that he will need to make using these recipes.

Q15:

A restaurant is promoting itself by serving a free drink to every 12th customer and a free meal to every 27th customer. Which customer will be the first to be served both a free meal and a free drink?

• A78th customer
• B324th customer
• C108th customer
• D39th customer
• E216th customer

Q16:

A TV show is giving away a discount coupon to every sixth caller and a free concert ticket to every tenth caller. Determine which caller will be the first to receive both a discount coupon and a free ticket.

Q17:

Which of the following describes all of the common multiples of 10 and 28? Note that is any positive, whole numbers.

• A
• B
• C
• D
• E

Q18:

Which of the following describes all of the common multiples of 12 and 21? Note that is any positive, whole numbers.

• A
• B
• C
• D
• E

Q19:

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?

Q20:

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.

• A17, 19
• B17, 18
• C18, 19
• D18, 18

Q21:

A normal speed printer prints an image every 19 seconds, and a more efficient one takes 6 seconds to print an image. If both printers start printing a document of identical images together, how many seconds will pass before the printers first complete printing out an image at the same time?

Q22:

In an inline speed skating competition, Jerry completes each lap in 25 seconds, Paul completes each lap in minutes, and Eugene completes each lap in 50 seconds. Given that they all start skating simultaneously, determine how many minutes will pass before they all cross the start line together again.

• A min
• B min
• C min
• D min

Q23:

Three cyclists ride their bicycles on a circular path. The first circles the path in 10 minutes, the second in 12 minutes, and the third in 40 minutes. If they all start at the same point and at the same time, and they all move in the same direction, in how many minutes will they meet again at the starting point?

Q24:

Complete the following table.

 First Number Second Number Greatest Common Factor Lowest Common Multiple 69 3 2 070 82 2 2 788
• A159, 150
• B90, 68
• C90, 150
• D159, 68

Q25:

Complete the following table.

 First Number Second Number Greatest Common Factor Lowest Common Multiple 48 2 2 352 44 4 88
• A146, 52
• B98, 8
• C98, 52
• D146, 8