Find Both the GCF and LCM
Written by Adi Ackerman, Head Teacher
"Find Both the GCF and LCM" is written for 6th Grade (Ages 11-12), and it covers Common Core 6.NS.B.4. If your student is a year younger but already steady on factoring, the page still works. You may just need to read the instructions out loud. And if they are older and greatest common factor (GCF) never quite stuck, this is a short review rather than busywork.
6th grade math worksheet: find both the GCF and the LCM of 12 pairs like 80 and 100 or 42 and 91. Answer key included. Part of our greatest common factor (GCF) factoring collection. Aligned to Common Core standards.
How do I use this worksheet?
Begin with the pairs to 50, where listing factors is quick. Move to three numbers and the GCF and LCM page once students can use prime factors.
What students will practice
- Students will find the GCF and the LCM of 12 pairs of numbers from 4 to 100.
- Students will use GCF × LCM = the product of the numbers, as in 2 × 12 = 4 × 6.
- Students will handle pairs with a GCF of 1, like 9 and 49 with an LCM of 441.
Greatest Common Factor of Two Numbers
Prime Factorization With Factor Trees
Divisibility Rules Practice
Find the Prime Factors of Numbers Under 400
Prime Factorization of Numbers Under 1,000
Write Prime Factorizations With Exponents
Greatest Common Factor of Numbers to 50
Greatest Common Factor of Three Numbers
Curriculum Links
Common Core State Standards
The Number System · 6th Grade
Standard: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
View all 6.NS.B.4 worksheets →Find this in the curriculum
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FAQ
How do I use this greatest common factor (GCF) worksheet?
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Begin with the pairs to 50, where listing factors is quick. Move to three numbers and the GCF and LCM page once students can use prime factors.
What does this worksheet teach?
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Find both the GCF and the LCM of 12 pairs like 80 and 100 or 42 and 91. For any two numbers, GCF × LCM equals the product of the numbers: for 4 and 6, 2 × 12 = 4 × 6. The directions on the page read: Find the greatest common factor (GCF) and the least common multiple (LCM) of each pair of numbers. An answer key is included.
Can I use this greatest common factor (GCF) worksheet for homeschool or classroom?
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Yes, both. We made it for 6th Grade factoring, and the page works the same whether it lands on a kitchen table or a center rotation. At home, most families go through it together and talk the answers out loud, and that talking is where most of the learning happens with greatest common factor (GCF). In class it runs well as independent work while you pull a small group. Print one copy or thirty, whichever the day needs.
How do you find the greatest common factor?
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List the factors of each number and pick the largest one they share, or multiply the prime factors they have in common. 80 = 2 to the 4th power × 5 and 48 = 2 to the 4th power × 3, so the GCF is 16.
Can the GCF be 1?
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Yes. When two numbers share no factor except 1, like 8 and 15 or 13 and 44, their GCF is 1.
How are the GCF and LCM related?
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For any two numbers, GCF × LCM equals the product of the numbers. For 4 and 6, 2 × 12 = 4 × 6 = 24.
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Greatest Common Factor of Two Numbers
Prime Factorization With Factor Trees
Divisibility Rules Practice
Find the Prime Factors of Numbers Under 400
Prime Factorization of Numbers Under 1,000
Write Prime Factorizations With Exponents
Greatest Common Factor of Numbers to 50
Greatest Common Factor of Three Numbers