GCF and LCM of 27 and 29

The GCF of 27 and 29 is 1. The LCM of 27 and 29 is 783.

27 and 29 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 27 × 29 = 783.

Method 1: list the factors (GCF)

Factors of 27: 1, 3, 9, 27.
Factors of 29: 1, 29.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

27 = 3 × 3 × 3
29 = 29 (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 × 3 × 3 × 29 = 783.

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. 29 = 1 × 27 + 2
  2. 27 = 13 × 2 + 1
  3. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(27, 29) = 1.

LCM by listing multiples

Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, ...
Multiples of 29: 29, 58, 87, 116, 145, 174, 203, 232, 261, ...
The first number in both lists is 783.

Check: GCF × LCM = product

1 × 783 = 783 = 27 × 29. This always holds for two numbers, so you can find the LCM as (27 × 29) ÷ 1 = 783.

Simplifying the fraction 27/29

27/29 is already in lowest terms because the GCF of 27 and 29 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 27154
3 and 27327
4 and 271108
5 and 271135
6 and 27354
7 and 271189
2 and 29158
3 and 29187
4 and 291116
5 and 291145
6 and 291174
7 and 291203

See also: factors of 27 · factors of 29.

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