GCF and LCM of 18 and 21

The GCF of 18 and 21 is 3. The LCM of 18 and 21 is 126.

• GCF (greatest common factor, also called GCD or HCF) of 18 and 21 = 3
• LCM (least common multiple) of 18 and 21 = 126

Method 1: list the factors (GCF)

Factors of 18: 1, 2, 3, 6, 9, 18.
Factors of 21: 1, 3, 7, 21.
Common factors: 1 and 3. The greatest of these is 3.

Method 2: prime factorization

18 = 2 × 3 × 3
21 = 3 × 7

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

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 3 × 3 × 7 = 126.

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. 21 = 1 × 18 + 3
2. 18 = 6 × 3 + 0

The last non-zero remainder is 3, so GCF(18, 21) = 3.

LCM by listing multiples

Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, ...
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, ...
The first number in both lists is 126.

Check: GCF × LCM = product

3 × 126 = 378 = 18 × 21. This always holds for two numbers, so you can find the LCM as (18 × 21) ÷ 3 = 126.

Simplifying the fraction 18/21

Divide the top and bottom by the GCF 3: 18/21 = 6/7.

GCF and LCM of similar pairs

See also: factors of 18 · factors of 21.

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