GCF and LCM Word Problems

In a clock, a larger gear completes a rotation every 45 seconds, and a small gear completes rotation every 18 seconds. If the gears are aligned now, how many seconds will pass before the gears are alligned?

• 90

• 89

• 9

• 8

Liller Billy is making activity baskets to donate to charity. She has 12 coloring books and 36 crayons. What is the greatest number of baskets she can make if each type of toy is equally distributed among the baskets?

• 2

• 12

• 36

• 6

A farmer needs to plant crops in a field every 18 days and another type of crop every 24 days. What is the least number of days after which he will need to plant both types of crops on the same day?

• 48

• 60

• 72

• 36

A school is planning a field trip for 36 students and needs to divide them into equal groups. What is the largest number of students they can have in each group?

• 24

• 18

• 12

• 6

A baker needs to package cookies in boxes of 15 and 20. What is the smallest number of cookies he can package so that there are an equal number of cookies in each box?

• 25

• 40

• 60

• 50

Big Billy went to the store and bought 15 oranges, 9 peaches, 18 watermelons he wants to put all of the fruit into a display at his market. Each display must have the same amount of fruit on each display. Without mixing fruits, what is the greatest number of pieces of fruit that Big Billy can put in each basket?

A factory produces products in batches of 30 and 45. What is the smallest number of products they can produce so that there are an equal number of products in each batch?

• 90

• 60

• 100

• 75

Hazel and Isabella are shelving books at the Sheppard library Hazel shelves 5 books at a time, where as Isabella shelves 6 books at a time. If they end up shelving the same number of books, what is the smallest number of books each could have shelved.

• LCM= 15 Books

• LCM= 12 Books

• LCM = 30 Books

• LCM= 24 Books

Lil Billy gets newsletters by e-mail. He gets one for sports every 5 days, and one for music every 8 days, and one for railroads every 10 days. If he got all three today, how many more days will it be until he gets all three newsletters on the same day again?

• 40

• 1

• 39

• 2

For a dinner party, Khoi is creating individual servings of starters. She has 9 carrot sticks and 18 celery sticks. If she wants each sering to be identical, with no food left over, what is the greatest number of servings Khoi can create?

• GCF= 36

• GCF= 18

• GCF= 27

• GCF= 9