GCF and LCM of 17 and 19

The GCF of 17 and 19 is 1. The LCM of 17 and 19 is 323.

• GCF (greatest common factor, also called GCD or HCF) of 17 and 19 = 1
• LCM (least common multiple) of 17 and 19 = 323

17 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: 17 × 19 = 323.

Method 1: list the factors (GCF)

Factors of 17: 1, 17.
Factors of 19: 1, 19.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

17 = 17 (prime)
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: 17 × 19 = 323.

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 × 17 + 2
2. 17 = 8 × 2 + 1
3. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(17, 19) = 1.

LCM by listing multiples

Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, ...
Multiples of 19: 19, 38, 57, 76, 95, 114, 133, 152, 171, ...
The first number in both lists is 323.

Check: GCF × LCM = product

1 × 323 = 323 = 17 × 19. This always holds for two numbers, so you can find the LCM as (17 × 19) ÷ 1 = 323.

Simplifying the fraction 17/19

17/19 is already in lowest terms because the GCF of 17 and 19 is 1.

GCF and LCM of similar pairs

See also: factors of 17 · factors of 19 · 17/19 as a decimal.

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