GCF and LCM of 10 and 19

The GCF of 10 and 19 is 1. The LCM of 10 and 19 is 190.

• GCF (greatest common factor, also called GCD or HCF) of 10 and 19 = 1
• LCM (least common multiple) of 10 and 19 = 190

10 and 19 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 10 × 19 = 190.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

10 = 2 × 5
19 = 19 (prime)

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 × 19 = 190.

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. 19 = 1 × 10 + 9
2. 10 = 1 × 9 + 1
3. 9 = 9 × 1 + 0

The last non-zero remainder is 1, so GCF(10, 19) = 1.

LCM by listing multiples

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, ...
The first number in both lists is 190.

Check: GCF × LCM = product

1 × 190 = 190 = 10 × 19. This always holds for two numbers, so you can find the LCM as (10 × 19) ÷ 1 = 190.

Simplifying the fraction 10/19

10/19 is already in lowest terms because the GCF of 10 and 19 is 1.

GCF and LCM of similar pairs

See also: factors of 10 · factors of 19 · 10/19 as a decimal.

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