GCF and LCM of 7 and 17

The GCF of 7 and 17 is 1. The LCM of 7 and 17 is 119.

7 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: 7 × 17 = 119.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

7 = 7 (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: 7 × 17 = 119.

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 × 7 + 3
  2. 7 = 2 × 3 + 1
  3. 3 = 3 × 1 + 0

The last non-zero remainder is 1, so GCF(7, 17) = 1.

LCM by listing multiples

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, ...
Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, ...
The first number in both lists is 119.

Check: GCF × LCM = product

1 × 119 = 119 = 7 × 17. This always holds for two numbers, so you can find the LCM as (7 × 17) ÷ 1 = 119.

Simplifying the fraction 7/17

7/17 is already in lowest terms because the GCF of 7 and 17 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 7114
3 and 7121
4 and 7128
5 and 7135
6 and 7142
7 and 8156
2 and 17134
3 and 17151
4 and 17168
5 and 17185
6 and 171102
8 and 171136

See also: factors of 7 · factors of 17 · 7/17 as a decimal.

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