GCF and LCM of 12 and 30

The GCF of 12 and 30 is 6. The LCM of 12 and 30 is 60.

Method 1: list the factors (GCF)

Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Common factors: 1, 2, 3 and 6. The greatest of these is 6.

Method 2: prime factorization

12 = 2 × 2 × 3
30 = 2 × 3 × 5

GCF: multiply the prime factors both numbers share: 2 × 3 = 6.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 5 = 60.

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 = 2 × 12 + 6
  2. 12 = 2 × 6 + 0

The last non-zero remainder is 6, so GCF(12, 30) = 6.

LCM by listing multiples

Multiples of 12: 12, 24, 36, 48, 60, 72, ...
Multiples of 30: 30, 60, 90, ...
The first number in both lists is 60.

Check: GCF × LCM = product

6 × 60 = 360 = 12 × 30. This always holds for two numbers, so you can find the LCM as (12 × 30) ÷ 6 = 60.

Simplifying the fraction 12/30

Divide the top and bottom by the GCF 6: 12/30 = 2/5.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 12212
3 and 12312
4 and 12412
5 and 12160
6 and 12612
7 and 12184
2 and 30230
3 and 30330
4 and 30260
5 and 30530
6 and 30630
7 and 301210

See also: factors of 12 · factors of 30.

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