GCF and LCM of 50 and 100

The GCF of 50 and 100 is 50. The LCM of 50 and 100 is 100.

• GCF (greatest common factor, also called GCD or HCF) of 50 and 100 = 50
• LCM (least common multiple) of 50 and 100 = 100

Method 1: list the factors (GCF)

Factors of 50: 1, 2, 5, 10, 25, 50.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1, 2, 5, 10, 25 and 50. The greatest of these is 50.

Method 2: prime factorization

50 = 2 × 5 × 5
100 = 2 × 2 × 5 × 5

GCF: multiply the prime factors both numbers share: 2 × 5 × 5 = 50.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 5 × 5 = 100.

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. 100 = 2 × 50 + 0

The last non-zero remainder is 50, so GCF(50, 100) = 50.

LCM by listing multiples

Multiples of 50: 50, 100, 150, ...
Multiples of 100: 100, 200, ...
The first number in both lists is 100.

Check: GCF × LCM = product

50 × 100 = 5,000 = 50 × 100. This always holds for two numbers, so you can find the LCM as (50 × 100) ÷ 50 = 100.

Simplifying the fraction 50/100

Divide the top and bottom by the GCF 50: 50/100 = 1/2.

GCF and LCM of similar pairs

See also: factors of 50 · factors of 100.

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