GCF and LCM of 18 and 22

The GCF of 18 and 22 is 2. The LCM of 18 and 22 is 198.

• GCF (greatest common factor, also called GCD or HCF) of 18 and 22 = 2
• LCM (least common multiple) of 18 and 22 = 198

Method 1: list the factors (GCF)

Factors of 18: 1, 2, 3, 6, 9, 18.
Factors of 22: 1, 2, 11, 22.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

18 = 2 × 3 × 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 × 3 × 11 = 198.

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 × 18 + 4
2. 18 = 4 × 4 + 2
3. 4 = 2 × 2 + 0

The last non-zero remainder is 2, so GCF(18, 22) = 2.

LCM by listing multiples

Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, ...
Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, ...
The first number in both lists is 198.

Check: GCF × LCM = product

2 × 198 = 396 = 18 × 22. This always holds for two numbers, so you can find the LCM as (18 × 22) ÷ 2 = 198.

Simplifying the fraction 18/22

Divide the top and bottom by the GCF 2: 18/22 = 9/11.

GCF and LCM of similar pairs

See also: factors of 18 · factors of 22.

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