Resources/GCF and LCM practice: factors and multiples
Grades 4-6•Printable worksheet + answer key•CC0 license

GCF and LCM practice: factors and multiples

A printable lesson focused on finding the greatest common factor and least common multiple.

Students learn systematic methods to find GCF and LCM using factor lists and prime factorization.

Print-ready worksheet with answer key and quick teaching tips.

Grades 4-60 problems10 minAnswer key included
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Ready-to-teach

Clear steps, examples, and practice in one printable page.

Misconception-proof

Highlights common mistakes and how to fix them quickly.

Open license

CC0: free to copy, adapt, and share without attribution.

Quick overview

This free GCF and LCM worksheet for grades 4-6 helps students master finding common factors and multiples with real-world applications.

Lesson plan snapshot

20-25 min
  • Warm-up (3 min): review factors vs multiples with a quick sort.
  • Model GCF (5 min): solve the worked example using factor lists.
  • Model LCM (5 min): solve an LCM example using multiples.
  • Guided practice (5 min): complete problems 1-4 as a group.
  • Independent practice (7 min): finish the remaining problems.

Materials: hundreds chart, factor tree template, pencil

Learning targets

  • List all factors of a number systematically.
  • Find the greatest common factor of two numbers.
  • Find the least common multiple of two numbers.
  • Apply GCF and LCM to word problems.

Step-by-step approach

  1. 1To find GCF: List all factors of both numbers, identify common factors, choose the greatest.
  2. 2To find LCM: List multiples of both numbers until you find the smallest common one.
  3. 3Alternative: Use prime factorization - GCF uses minimum powers, LCM uses maximum powers.
  4. 4Check: GCF × LCM = product of the two numbers.

Common mistakes

Mistake

Confusing GCF and LCM.

Try instead

GCF is a Factor (smaller, divides into both). LCM is a Multiple (larger, both divide into it).

Mistake

Assuming LCM is always the product.

Try instead

The product works, but often there's a smaller common multiple. Use: LCM = product ÷ GCF.

Mistake

Forgetting 1 and the number itself as factors.

Try instead

Always start with 1 and end with the number when listing factors.

Worked example

Guided
Find the GCF of 18 and 24.
  1. Factors of 18: 1, 2, 3, 6, 9, 18
  2. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
  3. Common factors: 1, 2, 3, 6
  4. Greatest common factor: 6
Answer: 6

Related resources

Fractions

GCF helps simplify fractions.

View resource

Division

Factor skills build on division fluency.

View resource

Multiplication

Multiple skills build on multiplication fluency.

View resource

Practice problems

14 problems • 21 min

Printable worksheet
  1. 1
    List all factors of 28.
  2. 2
    List the first 5 multiples of 8.
  3. 3
    List all factors of 18.
  4. 4
    Find the GCF of 24 and 24.
  5. 5
    Find the LCM of 3 and 4.
  6. 6
    List all factors of 15.
  7. 7
    Find the LCM of 12 and 18.
  8. 8
    List the first 5 multiples of 3.
  9. 9
    Find the GCF of 18 and 12.
  10. 10
    Find the LCM of 5 and 8.
  11. 11
    Find the GCF of 42 and 56.
  12. 12
    Bus A comes every 10 minutes. Bus B comes every 3 minutes. If both buses just arrived together, in how many minutes will they arrive together again?
  13. 13
    Find the LCM of 4 and 8.
  14. 14
    Find the GCF of 48 and 64.

Answer key

14 answers
  1. 11) 1, 2, 4, 7, 14, 28
  2. 22) 8, 16, 24, 32, 40
  3. 33) 1, 2, 3, 6, 9, 18
  4. 44) 24
  5. 55) 12
  6. 66) 1, 3, 5, 15
  7. 77) 36
  8. 88) 3, 6, 9, 12, 15
  9. 99) 6
  10. 1010) 40
  11. 1111) 14
  12. 1212) 30 minutes
  13. 1313) 8
  14. 1414) 16

Teacher tips

  • TUse Venn diagrams to visualize common factors.
  • TConnect GCF to simplifying fractions (GCF of 18/24 → 3/4).
  • TUse real scenarios: GCF for equal grouping, LCM for scheduling.

Parent tips

  • PPractice with small numbers first (GCF of 6 and 9).
  • PUse multiplication facts your child knows well.
  • PAsk: 'Does this answer make sense?' GCF should be smaller, LCM larger.

Open license

You are free to copy, adapt, and share these materials. No attribution required. Released under Creative Commons CC0 1.0 (public domain).