GCF and LCM of 22 and 50

The GCF of 22 and 50 is 2. The LCM of 22 and 50 is 550.

• GCF (greatest common factor, also called GCD or HCF) of 22 and 50 = 2
• LCM (least common multiple) of 22 and 50 = 550

Method 1: list the factors (GCF)

Factors of 22: 1, 2, 11, 22.
Factors of 50: 1, 2, 5, 10, 25, 50.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

22 = 2 × 11
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 × 5 × 5 × 11 = 550.

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 = 2 × 22 + 6
2. 22 = 3 × 6 + 4
3. 6 = 1 × 4 + 2
4. 4 = 2 × 2 + 0

The last non-zero remainder is 2, so GCF(22, 50) = 2.

LCM by listing multiples

Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, ...
Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, ...
The first number in both lists is 550.

Check: GCF × LCM = product

2 × 550 = 1,100 = 22 × 50. This always holds for two numbers, so you can find the LCM as (22 × 50) ÷ 2 = 550.

Simplifying the fraction 22/50

Divide the top and bottom by the GCF 2: 22/50 = 11/25.

GCF and LCM of similar pairs

See also: factors of 22 · factors of 50.

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