GCF and LCM of 12 and 60

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

• GCF (greatest common factor, also called GCD or HCF) of 12 and 60 = 12
• LCM (least common multiple) of 12 and 60 = 60

Method 1: list the factors (GCF)

Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors: 1, 2, 3, 4, 6 and 12. The greatest of these is 12.

Method 2: prime factorization

12 = 2 × 2 × 3
60 = 2 × 2 × 3 × 5

GCF: multiply the prime factors both numbers share: 2 × 2 × 3 = 12.

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. 60 = 5 × 12 + 0

The last non-zero remainder is 12, so GCF(12, 60) = 12.

LCM by listing multiples

Multiples of 12: 12, 24, 36, 48, 60, 72, ...
Multiples of 60: 60, 120, ...
The first number in both lists is 60.

Check: GCF × LCM = product

12 × 60 = 720 = 12 × 60. This always holds for two numbers, so you can find the LCM as (12 × 60) ÷ 12 = 60.

Simplifying the fraction 12/60

Divide the top and bottom by the GCF 12: 12/60 = 1/5.

GCF and LCM of similar pairs

See also: factors of 12 · factors of 60.

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