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GCF and LCM Worksheets

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Greatest common factor and least common multiple: listing factors and multiples, practice pairs, and word problems that ask which one you need.

Download the gcf and lcm worksheets

Greatest common factor

List the factors, then practice pairs.

Least common multiple

List the multiples, then practice pairs.

GCF and LCM together

Both for each pair, and word problems.

Print at 100% (actual size) for the cleanest tracing lines.

About these gcf and lcm worksheets

The greatest common factor (GCF) of two numbers is the biggest number that divides both of them. The GCF of 18 and 24 is 6. The least common multiple (LCM) is the smallest number that both numbers divide into. The LCM of 6 and 8 is 24.

Fifth graders use these ideas with fractions: the GCF simplifies 18/24 to 3/4, and the LCM gives the common denominator for adding 1/6 + 3/8. Listing the factors or the first ten multiples of each number is the clearest way to find them.

These pages start with listing factors and multiples, then practice pairs and word problems. The word problems mix both kinds, so children must decide whether a story asks for the greatest number of equal groups (GCF) or the next time things happen together (LCM). Every page has an answer key on page 2.

Standards

  • CCSS.MATH.CONTENT.6.NS.B.4Find 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 sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).
  • CCSS.MATH.CONTENT.4.OA.B.4Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its one-digit factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

How to use them

  1. Start with GCF: List the Factors and LCM: List the Multiples.
  2. Ask children to circle the common numbers in both lists before choosing.
  3. Move to the practice pages when listing is quick.
  4. Use the word problems last and ask children to explain their choice.

Teaching tips

  • The GCF is never bigger than the smaller number. The LCM is never 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" points to the GCF. "When will they next happen together" points to the LCM.

Questions teachers and parents ask

What is the difference between GCF and LCM?

The GCF is the greatest number that divides both numbers. The LCM is the least number that both numbers divide into.

Is GCF and LCM a 5th grade skill?

It is formally a 6th grade standard, but 5th graders use it for simplifying fractions and finding common denominators, so many classes start here.

How do you find the LCM quickly?

List the multiples of the bigger number and stop at the first one the smaller number divides into.