GCF and LCM of 21 and 27

The GCF of 21 and 27 is 3. The LCM of 21 and 27 is 189.

• GCF (greatest common factor, also called GCD or HCF) of 21 and 27 = 3
• LCM (least common multiple) of 21 and 27 = 189

Method 1: list the factors (GCF)

Factors of 21: 1, 3, 7, 21.
Factors of 27: 1, 3, 9, 27.
Common factors: 1 and 3. The greatest of these is 3.

Method 2: prime factorization

21 = 3 × 7
27 = 3 × 3 × 3

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

LCM: multiply every prime the maximum number of times it appears in either number: 3 × 3 × 3 × 7 = 189.

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. 27 = 1 × 21 + 6
2. 21 = 3 × 6 + 3
3. 6 = 2 × 3 + 0

The last non-zero remainder is 3, so GCF(21, 27) = 3.

LCM by listing multiples

Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, ...
Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, ...
The first number in both lists is 189.

Check: GCF × LCM = product

3 × 189 = 567 = 21 × 27. This always holds for two numbers, so you can find the LCM as (21 × 27) ÷ 3 = 189.

Simplifying the fraction 21/27

Divide the top and bottom by the GCF 3: 21/27 = 7/9.

GCF and LCM of similar pairs

See also: factors of 21 · factors of 27.

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