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GCF and LCM Worksheets

Ready-to-print worksheets

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Level 6

GCF and LCM worksheets teach students to find the greatest common factor and the least common multiple of two numbers, skills needed for simplifying fractions and adding fractions with unlike denominators. These free printable GCF and LCM worksheets cover factors, GCF, LCM, prime factorization and word problems, with an answer key on every PDF and a maker for new problems.

Quick answer: The GCF (greatest common factor) is the largest number that divides two numbers evenly, and the LCM (least common multiple) is the smallest number both divide into. For 12 and 18, the GCF is 6 and the LCM is 36. This page has 8 free GCF and LCM worksheets (PDF) with answer keys for grades 4 to 6, plus a maker. Updated October 2026.

Ready-to-print samples

A few of the ready PDFs on this page. The full list is under Ready-to-print worksheets, and the maker above makes new problems on demand.

gcf and lcm worksheets: factors of a number
Factors of a numberLevel 1 with a full answer key.PDF
greatest common factor worksheet
Greatest common factorLevel 2 with a full answer key.PDF
least common multiple worksheet
Least common multipleLevel 3 with a full answer key.PDF
prime factorization worksheet
Prime factorizationLevel 5 with a full answer key.PDF

How to find the GCF and LCM

  1. List the factors of each number, or write the prime factorization.
  2. GCF: pick the largest factor that appears in both lists, or multiply the shared prime factors.
  3. LCM: list multiples of each number until the first match, or multiply every prime factor the greatest number of times it appears.

GCF and LCM worksheet: six worked examples

Each row shows the prime factors, the GCF and the LCM. Notice that GCF × LCM always equals the product of the two numbers, which is a handy way to check:

Numbers Prime factors GCF LCM GCF × LCM
12 and 18 22 × 3; 2 × 32 6 36 216
24 and 36 23 × 3; 22 × 32 12 72 864
15 and 25 3 × 5; 52 5 75 375
16 and 40 24; 23 × 5 8 80 640
18 and 45 2 × 32; 32 × 5 9 90 810
28 and 42 22 × 7; 2 × 3 × 7 14 84 1176

Factors and multiples worksheet: what is the difference?

Factors divide a number evenly, so they are never larger than the number. Multiples are what you get by multiplying, so they are never smaller. These tables show both:

Number All factors Prime?
12 1, 2, 3, 4, 6, 12 No
17 1, 17 Yes
24 1, 2, 3, 4, 6, 8, 12, 24 No
30 1, 2, 3, 5, 6, 10, 15, 30 No
36 1, 2, 3, 4, 6, 9, 12, 18, 36 No
49 1, 7, 49 No
Number First six multiples
4 4, 8, 12, 16, 20, 24
6 6, 12, 18, 24, 30, 36
8 8, 16, 24, 32, 40, 48
9 9, 18, 27, 36, 45, 54
12 12, 24, 36, 48, 60, 72

Prime factorization worksheet: factor trees

Break a number into prime factors with a factor tree. Prime factorization is the quickest route to both the GCF and the LCM of larger numbers:

Number Factor tree Prime factorization
60 2 × 2 × 3 × 5 22 × 3 × 5
72 2 × 2 × 2 × 3 × 3 23 × 32
84 2 × 2 × 3 × 7 22 × 3 × 7
90 2 × 3 × 3 × 5 2 × 32 × 5
100 2 × 2 × 5 × 5 22 × 52
126 2 × 3 × 3 × 7 2 × 32 × 7

Try ten GCF and LCM problems

Use these as a warm-up. List factors or multiples on scratch paper if you need to.

# Problem Answer
1 GCF of 18 and 24 6
2 GCF of 28 and 42 14
3 GCF of 15 and 40 5
4 LCM of 6 and 8 24
5 LCM of 9 and 12 36
6 LCM of 5 and 7 35
7 Prime factorization of 48 24 × 3
8 Prime factorization of 90 2 × 32 × 5
9 Two buses leave together and return every 12 and 15 minutes. When are they together again? 60 minutes
10 Cut ribbons of 24 in and 36 in into equal pieces as long as possible 12 in pieces

GCF worksheet, greatest common factor worksheet and least common multiple worksheet

A GCF worksheet asks for the largest number that divides two or more numbers, so the answer is never larger than the smaller number. A greatest common factor worksheet usually starts with short lists of factors, then moves to prime factorization for larger numbers. A least common multiple worksheet works the other way: the answer is never smaller than the larger number, and it is found by listing multiples or combining prime factors.

An LCM worksheet and a GCF worksheet are often set together, because students mix the two up. The GCF and LCM worksheets on this page keep them apart at first and mix them at level 4, so students learn to decide which one a problem needs.

GCF and LCM word problems

GCF and LCM word problems hide the skill inside a story. If the problem asks for the largest equal groups or pieces, use the GCF. If it asks when two repeating events happen together again, use the LCM:

Word problem Skill needed Work Answer
A baker has 48 muffins and 72 cookies and makes identical boxes using all of them. How many boxes at most? GCF GCF of 48 and 72 24 boxes
One bell rings every 9 minutes and another every 12 minutes. When do they ring together? LCM LCM of 9 and 12 Every 36 minutes
Two ropes of 30 m and 45 m are cut into equal pieces, as long as possible. How long is each piece? GCF GCF of 30 and 45 15 m
Two runners lap a track in 5 and 7 minutes. When do they meet at the start? LCM LCM of 5 and 7 After 35 minutes

How to use these GCF and LCM worksheets

Use the GCF and LCM worksheets in order. Start with the factors sheet, then move to the greatest common factor, the least common multiple and prime factorization. Every one of the GCF and LCM worksheets has an answer key on the last page, so students can check their own work, and one short session is a good source of quick retests.

Once the methods are secure, finish with the word problem sheet. Print a GCF and LCM worksheet for homework and review it together the next day. Students who need more GCF and LCM worksheets can generate a new set in the maker, and GCF and LCM worksheets with fresh numbers make a reliable weekly check.

GCF and LCM vocabulary

Students answer questions faster when they know the words. These are the terms used on the worksheets and answer keys:

Word Meaning Example
Factor A number that divides another evenly 4 is a factor of 12
Multiple A product of a number and a whole number 12 is a multiple of 4
Prime number A number with exactly two factors, 1 and itself 2, 3, 5, 7, 11
Composite number A number with more than two factors 12
GCF The greatest common factor of two numbers GCF of 12 and 18 is 6
LCM The least common multiple of two numbers LCM of 12 and 18 is 36

Common Core standards for GCF and LCM

These worksheets practice the Common Core number system standards for grades 4 to 6:

Grade Standard What students do
Grade 4 4.OA.B.4 Find all factor pairs for a number from 1 to 100; recognize multiples and prime numbers
Grade 6 6.NS.B.4 Find the greatest common factor and the least common multiple of two whole numbers, and use the distributive property

Common mistakes with GCF and LCM

Mistake Example Fix
Mixing up GCF and LCM Finding 36 when asked for the GCF of 12 and 18 The GCF is the largest number that divides both: 6. The LCM is 36
Stopping at a common factor Taking 3 as the GCF of 12 and 18 Check for larger common factors: 6 divides both
Using the product as the LCM LCM of 6 and 8 = 48 List multiples: 24 is the first common one
Calling 1 a prime number Prime factors of 12 include 1 A prime has exactly two factors; 1 is not prime
Missing repeated primes 72 = 2 × 3 × 4 Break down fully: 72 = 23 × 32

Real-life uses of GCF and LCM

The GCF answers “what is the biggest group size”, and the LCM answers “when do things line up”:

Situation Skill Answer
Pack 24 pencils and 36 erasers into identical kits, using all of each GCF of 24 and 36 12 kits
Two lights blink every 6 and 8 seconds. When do they blink together? LCM of 6 and 8 24 seconds
Cut a 40 in board and a 56 in board into equal pieces, as long as possible GCF of 40 and 56 8 in pieces
Buses leave every 15 and 20 minutes from 8:00. Next time together? LCM of 15 and 20 9:00
Add 1/6 and 1/4 LCM of 6 and 4 Common denominator 12

Which GCF and LCM worksheet should you start with?

Start with factors, then GCF and LCM one at a time, and combine them at level 4. Set B gives a retest for levels 2 and 3.

Level Skill Best for
Level 1 Factors of a number Grades 4 and 5
Level 2 Greatest common factor Grade 6
Level 3 Least common multiple Grade 6
Level 4 GCF and LCM together Grade 6
Level 5 Prime factorization Grades 5 and 6
Level 6 Word problems Grade 6

A weekly plan for GCF and LCM

Day Focus Suggested block
Monday Factors and primes 15 min
Tuesday Greatest common factor 15 min
Wednesday Least common multiple 15 min
Thursday Prime factorization and word problems 15 min
Weekly total Four short sessions 60 min

Frequently asked questions

5 quick answers

Where can I download free GCF and LCM worksheets?

Open any worksheet in the Ready-to-print list on this page, choose US Letter or A4, then print or save the PDF. They are free, with answer keys, and no account is needed.

How do you find the GCF?

List the factors of each number and pick the largest one they share, or multiply the prime factors they have in common. The GCF of 24 and 36 is 12.

How do you find the LCM?

List multiples of each number until you find the first match. The LCM of 6 and 8 is 24.

What is the relationship between GCF and LCM?

For two numbers, GCF × LCM = the product of the numbers. For 12 and 18, 6 × 36 = 216 = 12 × 18.

What grade learns GCF and LCM?

Factors and multiples start in grade 4, and the GCF and LCM are grade 6 standards (6.NS.B.4).

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