GCF and LCM of 14 and 17

The GCF of 14 and 17 is 1. The LCM of 14 and 17 is 238.

• GCF (greatest common factor, also called GCD or HCF) of 14 and 17 = 1
• LCM (least common multiple) of 14 and 17 = 238

14 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: 14 × 17 = 238.

Method 1: list the factors (GCF)

Factors of 14: 1, 2, 7, 14.
Factors of 17: 1, 17.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

14 = 2 × 7
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 × 7 × 17 = 238.

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 × 14 + 3
2. 14 = 4 × 3 + 2
3. 3 = 1 × 2 + 1
4. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(14, 17) = 1.

LCM by listing multiples

Multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, ...
Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, ...
The first number in both lists is 238.

Check: GCF × LCM = product

1 × 238 = 238 = 14 × 17. This always holds for two numbers, so you can find the LCM as (14 × 17) ÷ 1 = 238.

Simplifying the fraction 14/17

14/17 is already in lowest terms because the GCF of 14 and 17 is 1.

GCF and LCM of similar pairs

See also: factors of 14 · factors of 17 · 14/17 as a decimal.

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