GCF and LCM of 6 and 17

The GCF of 6 and 17 is 1. The LCM of 6 and 17 is 102.

• GCF (greatest common factor, also called GCD or HCF) of 6 and 17 = 1
• LCM (least common multiple) of 6 and 17 = 102

6 and 17 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 6 × 17 = 102.

Method 1: list the factors (GCF)

Factors of 6: 1, 2, 3, 6.
Factors of 17: 1, 17.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

6 = 2 × 3
17 = 17 (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 × 3 × 17 = 102.

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. 17 = 2 × 6 + 5
2. 6 = 1 × 5 + 1
3. 5 = 5 × 1 + 0

The last non-zero remainder is 1, so GCF(6, 17) = 1.

LCM by listing multiples

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, ...
Multiples of 17: 17, 34, 51, 68, 85, 102, 119, ...
The first number in both lists is 102.

Check: GCF × LCM = product

1 × 102 = 102 = 6 × 17. This always holds for two numbers, so you can find the LCM as (6 × 17) ÷ 1 = 102.

Simplifying the fraction 6/17

6/17 is already in lowest terms because the GCF of 6 and 17 is 1.

GCF and LCM of similar pairs

See also: factors of 6 · factors of 17 · 6/17 as a decimal.

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