Greatest Common Factor and Least Common Multiple Word Problems

What is the greatest common factor of 30 and 84?

• 2

• 4

• 6

• 14

Jamie has 36 notebooks and 96 pencils. He wants to make packages to send to his cousins. Each package must have the same number of notebooks and pencils. What is the greatest number of packages that Jamie could make?

• 3

• 6

• 12

• 18

In a band camp, 36 students play a percussion instrument, and 96 students play a woodwind instrument. The director of a band camp wants to divide the students into small groups with the same number of students from each of the two sections in each group. What is the greatest number of groups that can be made and how many of each instrument will be in each group?

• 12 groups that include 6 percussion and 24 woodwind

• 4 groups that include 9 percussion and 24 woodwind

• 12 groups that include 3 percussion and 8 woodwind

• 4 groups that include 12 percussion and 30 woodwind

Rick wrote the following steps to find the greatest common factor of 42 and 70.

Step 1: List the factors of 70: 1, 2, 7, 10, 35, and 70.

Step 2: List the factors of 42: 1, 2, 3, 6, 7, 14, 21, and 42.

Step 3: List the common factors 70 and 42: 1 and 2.

Step 4: Find the greatest common factor: 2.

Which statement is true?

• Rick made a mistake. Rick did not include 21 as a factor of 70. The common factors of 42 and 70 are 1, 2, and 21. So the greatest common factor is 21 not 2.

• Rick made a mistake. Rick did not include 5 and 14 as the factors of 70. The common factors of 42 and 70 are 1, 2, 7, and 14. So the greatest common factor is 14 not 2.

• Rick made a mistake. Rick incorrectly listed the multiples instead of factors. The greatest common factor is 88 not 2.

• Rick made a mistake. Rick incorrectly listed the multiples instead of factors. The greatest common factor is 1,344 not 2.

Sara has 16 red flowers and 24 yellow flowers.  She wants to make bouquets with the same number of each color flow in each bouquet.  What is the greatest number of bouquets that she can make?

• Greatest Common Factor

• Least Common Multiple

• A

• B

• C

• D

What is the greatest common factor of 12x + 30

• 2

• 3

• 6

• 6x

greatest common factor of 24 and 48.

• 4

• 12

• 24

• 48

greatest common factor of 24 and 48.

• 4

• 12

• 24

• 48

What is the greatest common factor of 8 and 10?

• 1

• 3

• 4

• 2