GCF and LCM of 21 and 30

The GCF of 21 and 30 is 3. The LCM of 21 and 30 is 210.

Method 1: list the factors (GCF)

Factors of 21: 1, 3, 7, 21.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Common factors: 1 and 3. The greatest of these is 3.

Method 2: prime factorization

21 = 3 × 7
30 = 2 × 3 × 5

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 × 5 × 7 = 210.

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. 30 = 1 × 21 + 9
  2. 21 = 2 × 9 + 3
  3. 9 = 3 × 3 + 0

The last non-zero remainder is 3, so GCF(21, 30) = 3.

LCM by listing multiples

Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, ...
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, ...
The first number in both lists is 210.

Check: GCF × LCM = product

3 × 210 = 630 = 21 × 30. This always holds for two numbers, so you can find the LCM as (21 × 30) ÷ 3 = 210.

Simplifying the fraction 21/30

Divide the top and bottom by the GCF 3: 21/30 = 7/10.

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 30230
3 and 30330
4 and 30260
5 and 30530
6 and 30630
7 and 301210

See also: factors of 21 · factors of 30.

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