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Find the Greatest Common Factor and the Least Common Multiple

Show your factor lists or prime factorizations. Show your multiple lists for LCM problems.

Grade 6·21 problems·~35 min·Common Core Math - Grade 6·standard·6-ns-b-4
Work through problems with immediate feedback
A

Recall / Warm-Up

1.

Which of the following is a factor of 24?

2.

Which of the following is a multiple of 6?

3.

Apply the distributive property: 4×(9+2)=?4 \times (9 + 2) = ?

B

Fluency Practice

1.

Find GCF(24, 36) by listing factors.

2.

What is GCF(18, 45)?

Factor trees for 60 and 84 showing prime factorizations 2² × 3 × 5 and 2² × 3 × 7, with common factors 2² × 3 = 12 highlighted
3.

Use prime factorization to find GCF(60, 84).

4.

Find LCM(8, 12) by listing multiples of each number.

5.

Find LCM(5, 7).

C

Varied Practice

1.

What is GCF(56, 84)?

Number line from 0 to 24 showing multiples of 4 marked with circles at 4, 8, 12, 16, 20, 24 and multiples of 6 marked with squares at 6, 12, 18, 24 with the first overlap at 12 highlighted
2.

On the number line below, multiples of 4 are marked with circles (○) and multiples of 6 are marked with squares (□). The first number marked with both symbols is the LCM of 4 and 6:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   .

LCM(4, 6):
3.

What is LCM(9, 12)?

4.

Rewrite 36+836 + 8 using the GCF and the distributive property. GCF(36, 8) =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   . So 36 + 8 =   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   × (  ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   +   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲   ).

GCF:
GCF factor:
first quotient:
second quotient:
5.

A student rewrote 24+1824 + 18 as 2(12+9)2(12 + 9). Is this fully factored using the GCF?

D

Word Problems

1.

A baker has 48 chocolate chip cookies and 36 oatmeal cookies. She wants to arrange them into identical gift bags, with each bag containing only one type of cookie and each bag having the same number of cookies. No cookies are left over.

What is the greatest number of bags she can make?

2.

Bus A departs every 6 minutes. Bus B departs every 8 minutes. Both buses depart at 9:00 AM.

How many minutes after 9:00 AM will the buses next depart at the same time?

3.

A florist has 45 roses and 30 lilies. She wants to use all of them to make identical bouquets, with each bouquet containing the same combination of roses and lilies.

1.

What is the greatest number of bouquets she can make?

2.

Use the distributive property to rewrite 45+3045 + 30 using the GCF. What is the factored form?

E

Error Analysis

1.

Marcus was asked to find GCF(4, 6). He wrote: "Both 4 and 6 appear in the multiplication table. The smallest number that both 4 and 6 divide into is 12. So GCF(4, 6) = 12."

What error did Marcus make?

2.

Tasha rewrote 28+4228 + 42 as 2(14+21)2(14 + 21). She said: "I factored out 2 because both 28 and 42 are even. The factored form is 2(14+21)2(14 + 21)."

What error did Tasha make?

F

Challenge / Extension

1.

Find GCF(72, 96) using prime factorization. Show your work.

2.

A student factored 36+6036 + 60 as 6(6+10)6(6 + 10).
Greatest common factor:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  
Fully factored form:   ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲  

greatest common factor:
fully factored form:
0 of 21 answered