GCF and LCM of 14 and 50

The GCF of 14 and 50 is 2. The LCM of 14 and 50 is 350.

• GCF (greatest common factor, also called GCD or HCF) of 14 and 50 = 2
• LCM (least common multiple) of 14 and 50 = 350

Method 1: list the factors (GCF)

Factors of 14: 1, 2, 7, 14.
Factors of 50: 1, 2, 5, 10, 25, 50.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

14 = 2 × 7
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 × 7 = 350.

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

The last non-zero remainder is 2, so GCF(14, 50) = 2.

LCM by listing multiples

Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...
Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, ...
The first number in both lists is 350.

Check: GCF × LCM = product

2 × 350 = 700 = 14 × 50. This always holds for two numbers, so you can find the LCM as (14 × 50) ÷ 2 = 350.

Simplifying the fraction 14/50

Divide the top and bottom by the GCF 2: 14/50 = 7/25.

GCF and LCM of similar pairs

See also: factors of 14 · factors of 50.

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