GCF and LCM of 8 and 27

The GCF of 8 and 27 is 1. The LCM of 8 and 27 is 216.

8 and 27 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 8 × 27 = 216.

Method 1: list the factors (GCF)

Factors of 8: 1, 2, 4, 8.
Factors of 27: 1, 3, 9, 27.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

8 = 2 × 2 × 2
27 = 3 × 3 × 3

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 × 3 × 3 × 3 = 216.

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. 27 = 3 × 8 + 3
  2. 8 = 2 × 3 + 2
  3. 3 = 1 × 2 + 1
  4. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(8, 27) = 1.

LCM by listing multiples

Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, ...
Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, ...
The first number in both lists is 216.

Check: GCF × LCM = product

1 × 216 = 216 = 8 × 27. This always holds for two numbers, so you can find the LCM as (8 × 27) ÷ 1 = 216.

Simplifying the fraction 8/27

8/27 is already in lowest terms because the GCF of 8 and 27 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 27154
3 and 27327
4 and 271108
5 and 271135
6 and 27354
7 and 271189

See also: factors of 8 · factors of 27.

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