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GCF & LCM · Grades 7–7

GCF and LCM Worksheets

GCF is the largest number that divides both; LCM is the smallest that both divide into. The mix-up is close to universal, so these worksheets drill the difference.

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What it is

The greatest common factor (GCF) is the biggest number that divides both numbers; the least common multiple (LCM) is the smallest number both divide into. Prime factorization finds either one quickly.

Why it matters

GCF and LCM ask opposite questions — largest shared factor versus smallest shared multiple — and mixing up which one you need is what turns simplifying fractions into guesswork.

How to do it

  1. Write each number as a product of primes (e.g., 12 = 2² × 3).
  2. For the GCF, multiply the primes both share, using the lowest power of each.
  3. For the LCM, multiply every prime that appears, using the highest power of each.

Examples by level

  • BeginnerLCM of 2 and 6 =Answer6
  • IntermediateGCF of 2 and 8 =Answer2
  • AdvancedLCM of 16 and 40 =Answer80

Examples are generated by the same engine as the worksheets, so they're always mathematically correct. Built to avoid repeats, not reshuffle the same handful of questions.

Common mistakes

  • Confusing the GCF (a factor, so ≤ the numbers) with the LCM (a multiple, so ≥ the numbers).
  • Stopping at a common factor that isn't the greatest one.
  • Forgetting a prime factor when building the LCM.

Tips

  • The GCF is at most your smallest number; the LCM is at least your largest number.
  • If two numbers share no prime factors, their GCF is 1.

For parents

The GCF is smaller than or equal to your numbers; the LCM is larger than or equal. If your answer breaks that rule, you've mixed them up.

For teachers

Prime factorization makes both quick: the GCF multiplies the shared prime powers, the LCM multiplies the highest power of every prime that appears.

Key vocabulary

factor
a number that divides another with no remainder
multiple
the result of multiplying a number by a whole number

Frequently asked questions

What is the difference between GCF and LCM?
The GCF is the largest number that divides both (a common factor); the LCM is the smallest number both divide into (a common multiple).
How do you find the GCF with prime factorization?
Factor each number into primes, then multiply the primes they share, using the lowest power of each shared prime.

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