GCF and LCM of 27 and 30

The GCF of 27 and 30 is 3. The LCM of 27 and 30 is 270.

Method 1: list the factors (GCF)

Factors of 27: 1, 3, 9, 27.
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

27 = 3 × 3 × 3
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 × 3 × 3 × 5 = 270.

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 × 27 + 3
  2. 27 = 9 × 3 + 0

The last non-zero remainder is 3, so GCF(27, 30) = 3.

LCM by listing multiples

Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, ...
Multiples of 30: 30, 60, 90, 120, 150, 180, 210, 240, 270, ...
The first number in both lists is 270.

Check: GCF × LCM = product

3 × 270 = 810 = 27 × 30. This always holds for two numbers, so you can find the LCM as (27 × 30) ÷ 3 = 270.

Simplifying the fraction 27/30

Divide the top and bottom by the GCF 3: 27/30 = 9/10.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 27154
3 and 27327
4 and 271108
5 and 271135
6 and 27354
7 and 271189
2 and 30230
3 and 30330
4 and 30260
5 and 30530
6 and 30630
7 and 301210

See also: factors of 27 · factors of 30.

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