GCF and LCM of 6 and 12

The GCF of 6 and 12 is 6. The LCM of 6 and 12 is 12.

Method 1: list the factors (GCF)

Factors of 6: 1, 2, 3, 6.
Factors of 12: 1, 2, 3, 4, 6, 12.
Common factors: 1, 2, 3 and 6. The greatest of these is 6.

Method 2: prime factorization

6 = 2 × 3
12 = 2 × 2 × 3

GCF: multiply the prime factors both numbers share: 2 × 3 = 6.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 = 12.

Method 3: Euclidean algorithm (GCF)

Divide the larger number by the smaller and repeat with the remainder until it is 0. The last non-zero remainder is the GCF.

  1. 12 = 2 × 6 + 0

The last non-zero remainder is 6, so GCF(6, 12) = 6.

LCM by listing multiples

Multiples of 6: 6, 12, 18, ...
Multiples of 12: 12, 24, ...
The first number in both lists is 12.

Check: GCF × LCM = product

6 × 12 = 72 = 6 × 12. This always holds for two numbers, so you can find the LCM as (6 × 12) ÷ 6 = 12.

Simplifying the fraction 6/12

Divide the top and bottom by the GCF 6: 6/12 = 1/2.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 626
3 and 636
4 and 6212
5 and 6130
6 and 7142
6 and 8224
2 and 12212
3 and 12312
4 and 12412
5 and 12160
7 and 12184
8 and 12424

See also: factors of 6 · factors of 12 · 6/12 as a decimal.

Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.