GCF and LCM of 8 and 17

The GCF of 8 and 17 is 1. The LCM of 8 and 17 is 136.

8 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: 8 × 17 = 136.

Method 1: list the factors (GCF)

Factors of 8: 1, 2, 4, 8.
Factors of 17: 1, 17.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

8 = 2 × 2 × 2
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 × 2 × 17 = 136.

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 × 8 + 1
  2. 8 = 8 × 1 + 0

The last non-zero remainder is 1, so GCF(8, 17) = 1.

LCM by listing multiples

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, ...
Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, ...
The first number in both lists is 136.

Check: GCF × LCM = product

1 × 136 = 136 = 8 × 17. This always holds for two numbers, so you can find the LCM as (8 × 17) ÷ 1 = 136.

Simplifying the fraction 8/17

8/17 is already in lowest terms because the GCF of 8 and 17 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 828
3 and 8124
4 and 848
5 and 8140
6 and 8224
7 and 8156
2 and 17134
3 and 17151
4 and 17168
5 and 17185
6 and 171102
7 and 171119

See also: factors of 8 · factors of 17 · 8/17 as a decimal.

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