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.

How do you know whether a word problem needs the GCF or the LCM?

If you are splitting things into the greatest number of equal groups with none left over, use the GCF. If you are waiting for two repeating events to happen together again, or matching packs of different sizes, use the LCM.

Do these GCF and LCM worksheets come with answers?

Yes. The free Grade 7 sheets include their answer key, and every pack you make includes one too.

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. These worksheets drill the difference with two- and three-number questions, prime factorization, and word problems where choosing between them is the whole skill.

Generate gcf & lcm worksheets →

Free plan · 2 credits every month · answer keys included · no card required.

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. In a word problem, sharing into equal groups with nothing left over calls for the GCF; waiting until two things happen together again calls for the LCM.

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 and adding unlike fractions into guesswork.

How to do it

For small numbers, list them: the factors of each for the GCF, the first few multiples of each for the LCM.
For bigger numbers, use a factor tree: split off one prime at a time until every branch ends in a prime (60 = 2 × 30 = 2 × 2 × 15 = 2² × 3 × 5).
For the GCF, multiply the primes every number shares, using the lowest power of each.
For the LCM, multiply every prime that appears, using the highest power of each.
With three numbers, do the same: the GCF uses primes all three share; the LCM uses every prime from any of them.

Examples by level

BeginnerGCF of 20 and 26 =Answer2
IntermediateGCF of 4 and 26 =Answer2
AdvancedGCF of 40 and 48 =Answer8

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.
In a word problem, multiplying the two numbers instead of finding the LCM, which gives too big an answer whenever the numbers share a factor.

Tips

The GCF is at most your smallest number; the LCM is at least your largest number.
Check two numbers with GCF × LCM = the two numbers multiplied: 6 × 36 = 12 × 18 = 216.
Word-problem cues: 'greatest', 'equal groups', 'none left over' → GCF; 'next time', 'together again', 'fewest to match' → LCM.
If two numbers share no prime factors, their GCF is 1 and their LCM is their product.

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

Teach the word-problem cue first: equal groups with nothing left over is a GCF; two things lining up again is an LCM. Then a factor tree makes both quick, and GCF × LCM = the product of two numbers is a fast self-check.

Key vocabulary

factor: a number that divides another with no remainder
multiple: the result of multiplying a number by a whole number
prime number: a whole number greater than 1 whose only factors are 1 and itself
prime factorization: a number written as a product of primes, like 60 = 2² × 3 × 5
common factor: a number that is a factor of each of the numbers

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.
How do you know whether a word problem needs the GCF or the LCM?: If you are splitting things into the greatest number of equal groups with none left over, use the GCF. If you are waiting for two repeating events to happen together again, or matching packs of different sizes, use the LCM.
Do these GCF and LCM worksheets come with answers?: Yes. The free Grade 7 sheets include their answer key, and every pack you make includes one too.

Ready to practice?

Generate a print-ready gcf & lcm pack with answer keys: pick a grade and difficulty, and it's ready in seconds.

Create free worksheets

Free to start · answer keys included · free accounts get 5 Standard packs to use within 14 days · no card required.