GCF and LCM of 12 and 22

The GCF of 12 and 22 is 2. The LCM of 12 and 22 is 132.

• GCF (greatest common factor, also called GCD or HCF) of 12 and 22 = 2
• LCM (least common multiple) of 12 and 22 = 132

Method 1: list the factors (GCF)

Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 22: 1, 2, 11, 22.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

12 = 2 × 2 × 3
22 = 2 × 11

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

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 11 = 132.

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. 22 = 1 × 12 + 10
2. 12 = 1 × 10 + 2
3. 10 = 5 × 2 + 0

The last non-zero remainder is 2, so GCF(12, 22) = 2.

LCM by listing multiples

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, ...
Multiples of 22: 22, 44, 66, 88, 110, 132, 154, ...
The first number in both lists is 132.

Check: GCF × LCM = product

2 × 132 = 264 = 12 × 22. This always holds for two numbers, so you can find the LCM as (12 × 22) ÷ 2 = 132.

Simplifying the fraction 12/22

Divide the top and bottom by the GCF 2: 12/22 = 6/11.

GCF and LCM of similar pairs

See also: factors of 12 · factors of 22.

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