Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Looking for 6th grade greatest common factor and least common multiple? Then this Grade 6 lesson on Factors, Multiples and Common Ones: GCF and LCM explains each idea step by step, with worked examples.
Quick answer: The greatest common factor (GCF) of two whole numbers is the largest number that divides both with no remainder. The least common multiple (LCM) is the smallest positive number that both numbers divide into evenly. Prime factorization finds both, and the GCF also lets you rewrite a sum such as 36 + 8 as 4(9 + 2).
Standards: 6.NS.B.4 · Level: Grade 6
What are factors, multiples and prime factors?
- A factor of a number divides it with no remainder. The factors of 18 are 1, 2, 3, 6, 9 and 18.
- A multiple of a number is what you get when you multiply it by 1, 2, 3, and so on. Multiples of 7: 7, 14, 21, 28.
- A prime number has exactly two factors, 1 and itself. A composite number has more than two.
How do you find the greatest common factor with prime factorization?
A factor tree keeps splitting a number into smaller factors; each branch stops at a circled prime.
- Write each number as a product of primes using a factor tree.
- Circle the primes that appear in both lists, counting repeats.
- Multiply the shared primes.
48 = 2 × 2 × 2 × 2 × 3 and 72 = 2 × 2 × 2 × 3 × 3. Shared primes: 2, 2, 2 and 3. The GCF is 2 × 2 × 2 × 3 = 24.
How do you find the least common multiple?
Write out the multiples of each number until the two lists share a value. For 6 and 8, the first shared multiple is 24, so the LCM of 6 and 8 is 24.
| Idea | Goal | Result is |
|---|---|---|
| GCF | split into equal groups | never larger than the smaller number |
| LCM | find when events line up | never smaller than the larger number |
How does the GCF help you factor a sum?
Distributing in reverse lets you pull the GCF out of a sum. The GCF of 36 and 8 is 4, so 36 + 8 = 4 × 9 + 4 × 2 = 4(9 + 2).
Mixing up the two ideas. Reach for the GCF to share items into equal groups; reach for the LCM when two repeating cycles must coincide again.
Expand your factored answer. If it does not return the starting sum, a factor slipped away.
- A prime number has exactly two factors: 1 and itself.
- GCF = product of the primes the numbers share.
- LCM = the first multiple that appears in both lists.
- The GCF of two numbers is at most the smaller number; the LCM is at least the larger.
- A sum a + b can be written as GCF × (a ÷ GCF + b ÷ GCF).
Factors, Multiples and Common Ones: GCF and LCM: frequently asked questions
What is the difference between a factor and a multiple?
A factor divides a number evenly, so factors are smaller than or equal to it. A multiple is the number times a whole number, so multiples are larger than or equal to it. Factors of 12 include 4, while 48 is a multiple of 12.
Is 1 a prime number?
No. A prime has exactly two different factors, and 1 has only one factor. Because 1 is also not composite, it belongs to neither group.
When should I use the GCF and when the LCM?
Use the GCF to split quantities into the largest equal groups with nothing left over. Use the LCM to find when repeating events, such as bus schedules, happen together again.
What is the GCF of two numbers that share no prime factors?
The GCF is 1. For example, 15 and 28 share no primes, so their only common factor is 1. Such numbers are called relatively prime.
How do you factor 45 + 60 with the GCF?
The GCF of 45 and 60 is 15. Divide each term by 15 to get 3 and 4, so 45 + 60 = 15(3 + 4). Multiplying back gives 15 × 7 = 105, which checks.