GCF and LCM of 45 and 50

The GCF of 45 and 50 is 5. The LCM of 45 and 50 is 450.

• GCF (greatest common factor, also called GCD or HCF) of 45 and 50 = 5
• LCM (least common multiple) of 45 and 50 = 450

Method 1: list the factors (GCF)

Factors of 45: 1, 3, 5, 9, 15, 45.
Factors of 50: 1, 2, 5, 10, 25, 50.
Common factors: 1 and 5. The greatest of these is 5.

Method 2: prime factorization

45 = 3 × 3 × 5
50 = 2 × 5 × 5

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

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 3 × 3 × 5 × 5 = 450.

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 × 45 + 5
2. 45 = 9 × 5 + 0

The last non-zero remainder is 5, so GCF(45, 50) = 5.

LCM by listing multiples

Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...
Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, ...
The first number in both lists is 450.

Check: GCF × LCM = product

5 × 450 = 2,250 = 45 × 50. This always holds for two numbers, so you can find the LCM as (45 × 50) ÷ 5 = 450.

Simplifying the fraction 45/50

Divide the top and bottom by the GCF 5: 45/50 = 9/10.

GCF and LCM of similar pairs

See also: factors of 45 · factors of 50.

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