GCF and LCM of 3 and 17

The GCF of 3 and 17 is 1. The LCM of 3 and 17 is 51.

• GCF (greatest common factor, also called GCD or HCF) of 3 and 17 = 1
• LCM (least common multiple) of 3 and 17 = 51

3 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: 3 × 17 = 51.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

3 = 3 (prime)
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: 3 × 17 = 51.

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

The last non-zero remainder is 1, so GCF(3, 17) = 1.

LCM by listing multiples

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, ...
Multiples of 17: 17, 34, 51, 68, ...
The first number in both lists is 51.

Check: GCF × LCM = product

1 × 51 = 51 = 3 × 17. This always holds for two numbers, so you can find the LCM as (3 × 17) ÷ 1 = 51.

Simplifying the fraction 3/17

3/17 is already in lowest terms because the GCF of 3 and 17 is 1.

GCF and LCM of similar pairs

See also: factors of 3 · factors of 17 · 3/17 as a decimal.

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