GCF and LCM of 50 and 60

The GCF of 50 and 60 is 10. The LCM of 50 and 60 is 300.

• GCF (greatest common factor, also called GCD or HCF) of 50 and 60 = 10
• LCM (least common multiple) of 50 and 60 = 300

Method 1: list the factors (GCF)

Factors of 50: 1, 2, 5, 10, 25, 50.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors: 1, 2, 5 and 10. The greatest of these is 10.

Method 2: prime factorization

50 = 2 × 5 × 5
60 = 2 × 2 × 3 × 5

GCF: multiply the prime factors both numbers share: 2 × 5 = 10.

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. 60 = 1 × 50 + 10
2. 50 = 5 × 10 + 0

The last non-zero remainder is 10, so GCF(50, 60) = 10.

LCM by listing multiples

Multiples of 50: 50, 100, 150, 200, 250, 300, 350, ...
Multiples of 60: 60, 120, 180, 240, 300, 360, ...
The first number in both lists is 300.

Check: GCF × LCM = product

10 × 300 = 3,000 = 50 × 60. This always holds for two numbers, so you can find the LCM as (50 × 60) ÷ 10 = 300.

Simplifying the fraction 50/60

Divide the top and bottom by the GCF 10: 50/60 = 5/6.

GCF and LCM of similar pairs

See also: factors of 50 · factors of 60.

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