GCF and LCM of 19 and 50

The GCF of 19 and 50 is 1. The LCM of 19 and 50 is 950.

• GCF (greatest common factor, also called GCD or HCF) of 19 and 50 = 1
• LCM (least common multiple) of 19 and 50 = 950

19 and 50 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 19 × 50 = 950.

Method 1: list the factors (GCF)

Factors of 19: 1, 19.
Factors of 50: 1, 2, 5, 10, 25, 50.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

19 = 19 (prime)
50 = 2 × 5 × 5

GCF: multiply the prime factors both numbers share: there are none, so the GCF is 1.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 5 × 5 × 19 = 950.

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 × 19 + 12
2. 19 = 1 × 12 + 7
3. 12 = 1 × 7 + 5
4. 7 = 1 × 5 + 2
5. 5 = 2 × 2 + 1
6. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(19, 50) = 1.

LCM by listing multiples

Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, ...
Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, ...
The first number in both lists is 950.

Check: GCF × LCM = product

1 × 950 = 950 = 19 × 50. This always holds for two numbers, so you can find the LCM as (19 × 50) ÷ 1 = 950.

Simplifying the fraction 19/50

19/50 is already in lowest terms because the GCF of 19 and 50 is 1.

GCF and LCM of similar pairs

See also: factors of 19 · factors of 50 · 19/50 as a decimal.

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