GCF and LCM of 21 and 36

The GCF of 21 and 36 is 3. The LCM of 21 and 36 is 252.

Method 1: list the factors (GCF)

Factors of 21: 1, 3, 7, 21.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Common factors: 1 and 3. The greatest of these is 3.

Method 2: prime factorization

21 = 3 × 7
36 = 2 × 2 × 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: 2 × 2 × 3 × 3 × 7 = 252.

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. 36 = 1 × 21 + 15
  2. 21 = 1 × 15 + 6
  3. 15 = 2 × 6 + 3
  4. 6 = 2 × 3 + 0

The last non-zero remainder is 3, so GCF(21, 36) = 3.

LCM by listing multiples

Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, ...
Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, ...
The first number in both lists is 252.

Check: GCF × LCM = product

3 × 252 = 756 = 21 × 36. This always holds for two numbers, so you can find the LCM as (21 × 36) ÷ 3 = 252.

Simplifying the fraction 21/36

Divide the top and bottom by the GCF 3: 21/36 = 7/12.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 21142
3 and 21321
4 and 21184
5 and 211105
6 and 21342
7 and 21721
2 and 36236
3 and 36336
4 and 36436
5 and 361180
6 and 36636
7 and 361252

See also: factors of 21 · factors of 36.

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