GCF and LCM of 6 and 22

The GCF of 6 and 22 is 2. The LCM of 6 and 22 is 66.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

6 = 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 × 3 × 11 = 66.

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 = 3 × 6 + 4
  2. 6 = 1 × 4 + 2
  3. 4 = 2 × 2 + 0

The last non-zero remainder is 2, so GCF(6, 22) = 2.

LCM by listing multiples

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, ...
Multiples of 22: 22, 44, 66, 88, ...
The first number in both lists is 66.

Check: GCF × LCM = product

2 × 66 = 132 = 6 × 22. This always holds for two numbers, so you can find the LCM as (6 × 22) ÷ 2 = 66.

Simplifying the fraction 6/22

Divide the top and bottom by the GCF 2: 6/22 = 3/11.

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 22222
3 and 22166
4 and 22244
5 and 221110
7 and 221154
8 and 22288

See also: factors of 6 · factors of 22.

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