GCF and LCM of 8 and 22

The GCF of 8 and 22 is 2. The LCM of 8 and 22 is 88.

Method 1: list the factors (GCF)

Factors of 8: 1, 2, 4, 8.
Factors of 22: 1, 2, 11, 22.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

8 = 2 × 2 × 2
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 × 2 × 11 = 88.

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 = 2 × 8 + 6
  2. 8 = 1 × 6 + 2
  3. 6 = 3 × 2 + 0

The last non-zero remainder is 2, so GCF(8, 22) = 2.

LCM by listing multiples

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, ...
Multiples of 22: 22, 44, 66, 88, 110, ...
The first number in both lists is 88.

Check: GCF × LCM = product

2 × 88 = 176 = 8 × 22. This always holds for two numbers, so you can find the LCM as (8 × 22) ÷ 2 = 88.

Simplifying the fraction 8/22

Divide the top and bottom by the GCF 2: 8/22 = 4/11.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 828
3 and 8124
4 and 848
5 and 8140
6 and 8224
7 and 8156
2 and 22222
3 and 22166
4 and 22244
5 and 221110
6 and 22266
7 and 221154

See also: factors of 8 · factors of 22.

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