GCF and LCM of 12 and 17

The GCF of 12 and 17 is 1. The LCM of 12 and 17 is 204.

• GCF (greatest common factor, also called GCD or HCF) of 12 and 17 = 1
• LCM (least common multiple) of 12 and 17 = 204

12 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: 12 × 17 = 204.

Method 1: list the factors (GCF)

Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 17: 1, 17.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

12 = 2 × 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 × 2 × 3 × 17 = 204.

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 = 1 × 12 + 5
2. 12 = 2 × 5 + 2
3. 5 = 2 × 2 + 1
4. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(12, 17) = 1.

LCM by listing multiples

Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, ...
Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, ...
The first number in both lists is 204.

Check: GCF × LCM = product

1 × 204 = 204 = 12 × 17. This always holds for two numbers, so you can find the LCM as (12 × 17) ÷ 1 = 204.

Simplifying the fraction 12/17

12/17 is already in lowest terms because the GCF of 12 and 17 is 1.

GCF and LCM of similar pairs

See also: factors of 12 · factors of 17 · 12/17 as a decimal.

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