Least Common Multiple Word Problems

Sarah practices piano every 5 days and guitar every 8 days. If she wants to practice both instruments on the same day, what is the smallest number of days she needs to wait before she can do both activities again?

• 5

• 8

• 10

• 40

Answer explanation

Sarah practices piano every 5 days and guitar every 8 days. You need to find the smallest number of days she needs to wait before she can do both activities on the same day again.

To find the LCM of 5 and 8, list the multiples of each number and look for the smallest common multiple.

The multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40 ...

The multiples of 8 are: 8, 16, 24, 32, 40 ...

From the listed multiples, the smallest number appearing in both lists is 40. Therefore, Sarah needs to wait for 40 days before she can practice piano and guitar on the same day again.

John eats dinner every 18 days and goes to the cinema every 24 days. If he wants to eat dinner and go to the cinema on the same day, what is the smallest number of days he needs to wait before he can do both activities again?

• 36

• 48

• 72

• 96

Answer explanation

John eats dinner every 18 days and goes to the cinema every 24 days. You can list the multiples of each number and look for the smallest common multiple.

The multiples of 18 are: 18, 36, 54, 72, 90, 108, ...

The multiples of 24 are: 24, 48, 72, 96, 120, 144, ...

From the listed multiples, the smallest number appearing in both lists is 72. Therefore, John needs to wait for 72 days before he can eat dinner and go to the cinema on the same day again.

Emily buys groceries every 4 days and does laundry every 6 days. If she wants to do both tasks on the same day, what is the smallest number of days she needs to wait before she can do both activities again?

• 12

• 8

• 6

• 24

Answer explanation

Emily buys groceries every 4 days and does laundry every 6 days. You need to find the smallest number of days she needs to wait before she can do both tasks on the same day again.

To find the LCM of 4 and 6, list the multiples of each number and look for the smallest common multiple.

The multiples of 4 are: 4, 8, 12, 16, 20, 24, ...

The multiples of 6 are: 6, 12, 18, 24, 30, 36, ...

From the listed multiples, the smallest number appearing in both lists is 12. Therefore, Emily needs to wait for 12 days before she can buy groceries and do laundry on the same day again.

Daniel goes hiking every 32 days and goes camping every 48 days. If he wants to go hiking and go camping on the same day, what is the smallest number of days he needs to wait before he can do both activities again?

• 256

• 128

• 96

• 64

Answer explanation

Daniel goes hiking every 32 days and goes camping every 48 days.

The multiples of 32 are: 32, 64, 96, 128, 160, 192, ...

The multiples of 48 are: 48, 96, 144, 192, 240, 288, ...

From the listed multiples, the smallest number appearing in both lists is 96. Therefore, Daniel needs to wait for 96 days before he can go hiking and go camping on the same day again.

Lily waters her plants every 6 days and fertilizes them every 9 days. If she wants to water and fertilize her plants on the same day, what is the smallest number of days she needs to wait before she can do both activities again?

• 9

• 18

• 15

• 54

Answer explanation

Lily waters her plants every 6 days and fertilizes them every 9 days. You need to find the smallest number of days she needs to wait before she can do both activities on the same day again.

To find the LCM of 6 and 9, list the multiples of each number and look for the smallest common multiple.

The multiples of 6 are: 6, 12, 18, 24, 30, 36, ...

The multiples of 9 are: 9, 18, 27, 36, 45, 54, ...

From the listed multiples, the smallest number appearing in both lists is 18. Therefore, Lily needs to wait for 18 days before she can water and fertilize her plants on the same day again.