6th Grade GCF, LCM, and Equivalent Expressions Worksheets

What students practice

Students list factors and multiples, finish prime factor trees, and find the GCF of two numbers up to 100 and the LCM of two numbers up to 12. Word problems ask whether things are shared equally or repeat until they meet before any arithmetic. The second half combines like terms, multiplies each term inside parentheses, reads area models, factors out the GCF, and tests expressions with numbers to decide whether they are equivalent.

What's inside

1. p. 3

   Factors and the GCF

   • 6.PAR.6.2

   List the factors of each number, then write the greatest common factor.

2. p. 4

   Prime Factor Trees

   • 6.PAR.6.2

   Finish each factor tree, then use prime factors to find each GCF.

3. p. 5

   Multiples and the LCM

   • 6.PAR.6.2

   List multiples of each number, then write the least common multiple.

4. p. 6

   GCF and LCM Code

   • 6.PAR.6.2

   Find each GCF or LCM, then use the code to find the hidden word.

5. p. 7

   GCF and LCM Word Problems

   • 6.PAR.6.2

   Decide whether each problem needs a GCF or an LCM, then solve it.

6. p. 8

   Factor a Sum With the GCF

   • 6.PAR.6.2

   Write each sum as the GCF times a sum, then answer the last question.

7. p. 9

   Combine Like Terms

   • 6.PAR.6.5

   Combine like terms to write an equivalent expression.

8. p. 10

   Multiply Each Term

   • 6.PAR.6.5

   Multiply each term inside the parentheses to write an equivalent expression.

9. p. 11

   Area Models

   • 6.PAR.6.5

   Use each area model to write the area as a product and as a sum.

10. p. 12

    Factor Out the GCF

    • 6.PAR.6.5

    Use the GCF to write each expression as a product, then answer the last question.

11. p. 13

    Equivalent or Not

    • 6.PAR.6.5

    Find the value of each expression for both values, then decide.

12. p. 14

    Mixed Review

    • 6.PAR.6.2
    • 6.PAR.6.5

    Solve each problem, then check your work.

Georgia standards covered

Who it's for

Grade 6 classes on factors, multiples, and equivalent expressions, usually after our Exponents and Expressions packet. Students never have to name a property, and no coefficient is negative.

More Grade 6 packets

• Expressions: Exponents, Writing, and Evaluating6.PAR.6.1 · 6.PAR.6.3 · 6.PAR.6.4
• One-Step Equations: Substitute, Write, and Solve6.PAR.7.1 · 6.PAR.7.2 · 6.PAR.7.3
• Inequalities: Solutions, Situations, and Number Lines6.PAR.7.1 · 6.PAR.7.2 · 6.PAR.7.4

All Grade 6 packets · Grade 6 standards by code