GCF and LCM of 12 and 50

The GCF of 12 and 50 is 2. The LCM of 12 and 50 is 300.

• GCF (greatest common factor, also called GCD or HCF) of 12 and 50 = 2
• LCM (least common multiple) of 12 and 50 = 300

Method 1: list the factors (GCF)

Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 50: 1, 2, 5, 10, 25, 50.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

12 = 2 × 2 × 3
50 = 2 × 5 × 5

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

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 5 × 5 = 300.

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. 50 = 4 × 12 + 2
2. 12 = 6 × 2 + 0

The last non-zero remainder is 2, so GCF(12, 50) = 2.

LCM by listing multiples

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, ...
Multiples of 50: 50, 100, 150, 200, 250, 300, 350, ...
The first number in both lists is 300.

Check: GCF × LCM = product

2 × 300 = 600 = 12 × 50. This always holds for two numbers, so you can find the LCM as (12 × 50) ÷ 2 = 300.

Simplifying the fraction 12/50

Divide the top and bottom by the GCF 2: 12/50 = 6/25.

GCF and LCM of similar pairs

See also: factors of 12 · factors of 50.

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