GCF and LCM of 36 and 50

The GCF of 36 and 50 is 2. The LCM of 36 and 50 is 900.

• GCF (greatest common factor, also called GCD or HCF) of 36 and 50 = 2
• LCM (least common multiple) of 36 and 50 = 900

Method 1: list the factors (GCF)

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 50: 1, 2, 5, 10, 25, 50.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

36 = 2 × 2 × 3 × 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 × 3 × 5 × 5 = 900.

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 = 1 × 36 + 14
2. 36 = 2 × 14 + 8
3. 14 = 1 × 8 + 6
4. 8 = 1 × 6 + 2
5. 6 = 3 × 2 + 0

The last non-zero remainder is 2, so GCF(36, 50) = 2.

LCM by listing multiples

Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, ...
Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, ...
The first number in both lists is 900.

Check: GCF × LCM = product

2 × 900 = 1,800 = 36 × 50. This always holds for two numbers, so you can find the LCM as (36 × 50) ÷ 2 = 900.

Simplifying the fraction 36/50

Divide the top and bottom by the GCF 2: 36/50 = 18/25.

GCF and LCM of similar pairs

See also: factors of 36 · factors of 50.

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