GCF and LCM worksheet

Grade 6 math, Common Core 6.NS.B.4. 10 problems with an answer key and worked steps. Free to print, and you can make new problems any time.

By the StudyWiz teamUpdated October 23, 2026How we write our pages

Print the answer key

NameDate

GCF and LCM

Grade 6 math, Common Core 6.NS.B.4

Find the greatest common factor (GCF) or least common multiple (LCM).

1.
Find the GCF of 15 and 40.
2.
Nia has 18 apples and 21 oranges. What is the greatest number of identical fruit bags that can be made, using all the fruit?
3.
Find the LCM of 6 and 14.
4.
Hot dogs come in packs of 6 and buns in packs of 8. What is the smallest number of each you can buy to have the same number of hot dogs and buns?
5.
Use the GCF to write 30 + 18 as a product, like 4(2 + 3).
6.
Use the GCF to write 48 + 42 as a product, like 4(2 + 3).
7.
Leo has 56 apples and 16 oranges. What is the greatest number of identical fruit bags that can be made, using all the fruit?
8.
Nia has 30 apples and 70 oranges. What is the greatest number of identical fruit bags that can be made, using all the fruit?
9.
Hot dogs come in packs of 10 and buns in packs of 12. What is the smallest number of each you can buy to have the same number of hot dogs and buns?
10.
Noah has 20 apples and 15 oranges. What is the greatest number of identical fruit bags that can be made, using all the fruit?

Answer key: GCF and LCM

Grade 6 math. Each answer has a few worked steps, to help check the method as well as the answer.

1. 5
15 = 5 × 3, 40 = 5 × 83 and 8 have no common factor, so the GCF is 5
2. 3 bags
GCF of 18 and 21 is 3Each bag gets 6 apples and 7 oranges
3. 42
Multiples of 14: 14, 28, 42, 56…The first one 6 divides is 42
4. 24 of each
LCM of 6 and 8 is 244 packs of hot dogs and 3 packs of buns
5. 6(5 + 3)
The GCF of 30 and 18 is 630 + 18 = 6(5 + 3)
6. 6(8 + 7)
The GCF of 48 and 42 is 648 + 42 = 6(8 + 7)
7. 8 bags
GCF of 56 and 16 is 8Each bag gets 7 apples and 2 oranges
8. 10 bags
GCF of 30 and 70 is 10Each bag gets 3 apples and 7 oranges
9. 60 of each
LCM of 10 and 12 is 606 packs of hot dogs and 5 packs of buns
10. 5 bags
GCF of 20 and 15 is 5Each bag gets 4 apples and 3 oranges

The answer key prints on its own page. You’re welcome to print and copy these worksheets for your own kids or class.

About GCF and LCM

The greatest common factor of two numbers is the biggest number that divides both of them. The least common multiple is the smallest number both of them divide into. You can find them by listing factors or multiples, or by using prime factorization. GCF problems are about splitting things into equal groups; LCM problems are about things lining up again.

Worked example 1

Find the LCM of 6 and 10.

Step 1.Multiples of 10: 10, 20, 30, 40…
Step 2.The first one 6 divides is 30

Answer: 30

Worked example 2

Diego has 84 apples and 72 oranges. What is the greatest number of identical fruit bags that can be made, using all the fruit?

Step 1.GCF of 84 and 72 is 12
Step 2.Each bag gets 7 apples and 6 oranges

Answer: 12 bags

Worked example 3

Use the GCF to write 16 + 56 as a product, like 4(2 + 3).

Step 1.The GCF of 16 and 56 is 8
Step 2.16 + 56 = 8(2 + 7)

Answer: 8(2 + 7)

Watch out for

The GCF can never be bigger than the smaller number. The LCM can never be smaller than the bigger number.
If one number divides the other, the smaller one is the GCF and the bigger one is the LCM.
“Greatest number of identical groups” is a GCF problem. “When will they match up” is an LCM problem.

Practice GCF and LCM online

On StudyWiz, your kid can practice GCF and LCM with 5-question quizzes that are checked as they go, with an explanation for every answer. When a homework problem is the trouble, Wiz gives a hint for each step instead of the answer.

Keep reading

Try Wiz with tonight’s homework

Free to start, no card needed. Each kid gets 3 homework questions, 5 practice quizzes and 1 writing review a day on the free plan.

Start free See pricing