Skip to main content
Common Core Math6th GradeThe Number System

6.NS.4: Greatest Common Factor and Least Common Multiple

Also written as 6.NS.B.4 and CCSS.MATH.CONTENT.6.NS.B.4 · Cluster: Compute fluently with multi-digit numbers and find common factors and multiples.

All 29 6th Grade Math Standards

The Official Wording

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. For example, express 36 + 8 as 4 (9 + 2)..

Common Core State Standards, Grade 6, The Number System · Read it at the source · Checked October 14, 2026

What 6.NS.4 Means in Plain English

Sixth graders find the greatest common factor of numbers up to 100, like 12 for 48 and 60, and the least common multiple of numbers up to 12, like 24 for 8 and 12. The GCF then factors a sum: 48 + 60 = 12 (4 + 5).

The distributive-property piece is the point: pulling out a common factor is the first factoring students do, and 6.EE.3 asks for it with variables the same year. The LCM returns whenever fractions need a common denominator, and in 7th grade 7.EE.1 factors expressions with rational coefficients.

6.NS.4 I Can Statements

  • I can find the greatest common factor of two numbers up to 100.
  • I can find the least common multiple of two numbers up to 12.
  • I can pull a common factor out of a sum of two numbers.

6.NS.4 Worked Example

One pile of snacks answers two questions: the greatest common factor, and the sum rewritten with that factor outside the parentheses.

Problem

A teacher has 48 pretzels and 60 crackers and wants identical snack bags with nothing left over. What is the greatest number of bags she can make, and what goes in each? Then write 48 + 60 using that number.

Identical snack bags from 48 pretzels and 60 crackers
  1. The greatest number of identical bags is the greatest common factor of 48 and 60. List the factors of each.48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 and 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
  2. The biggest number on both lists is 12.GCF(48, 60) = 12, so 12 bags
  3. Divide each snack by 12 to fill a bag.48 ÷ 12 = 4 pretzels and 60 ÷ 12 = 5 crackers per bag
  4. Now the distributive property: 12 bags of (4 + 5) snacks is the same total as 48 + 60.48 + 60 = 12 × 4 + 12 × 5 = 12 (4 + 5)
  5. Check that 4 and 5 share no factor but 1, or the factoring is not finished.GCF(4, 5) = 1
Answer12 bags, each with 4 pretzels and 5 crackers, and 48 + 60 = 12 (4 + 5)

Check it: 12 × (4 + 5) = 12 × 9 = 108, and 48 + 60 = 108.

Common Mistakes with 6.NS.4

Mixing up GCF and LCM

“The GCF of 8 and 12 is 24”

Try this: Say the names in full. A factor divides the number, so it cannot be bigger. A multiple is at least as big.

Stopping at a common factor that is not the greatest

48 + 60 = 4 (12 + 15)

Try this: Check the two numbers inside the parentheses. 12 and 15 still share 3, so pull it out too: 12 (4 + 5).

Multiplying to get the LCM

“The LCM of 6 and 9 is 54”

Try this: List the multiples of the larger number first, 9, 18, 27, and stop at the first one that 6 also divides: 18.

Where 6.NS.4 Fits

Comes Before4.OA.4Find all factor pairs of a number up to 100 and tell prime from composite.3.OA.5Use the distributive property to multiply.5.NF.1Add fractions with unlike denominators by finding a common denominator.
Alongside6.EE.3Factor an expression with the distributive property, like 24x + 18y = 6 (4x + 3y).6.NS.1Simplify fraction quotients with common factors.
Comes Next7.EE.1Add, subtract, factor and expand linear expressions with rational coefficients.

Practice 6.NS.4

Quick Check

  1. Find the GCF of 36 and 54.
  2. Find the LCM of 6 and 10.
  3. Write 56 + 72 as a multiple of a sum of two numbers with no common factor.

6.NS.4: Other Names

6.NS.46.NS.B.4CCSS.MATH.CONTENT.6.NS.B.4

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.