GCF and LCM of 27 and 28

The GCF of 27 and 28 is 1. The LCM of 27 and 28 is 756.

• GCF (greatest common factor, also called GCD or HCF) of 27 and 28 = 1
• LCM (least common multiple) of 27 and 28 = 756

27 and 28 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 27 × 28 = 756.

Method 1: list the factors (GCF)

Factors of 27: 1, 3, 9, 27.
Factors of 28: 1, 2, 4, 7, 14, 28.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

27 = 3 × 3 × 3
28 = 2 × 2 × 7

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 × 3 × 3 × 3 × 7 = 756.

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. 28 = 1 × 27 + 1
2. 27 = 27 × 1 + 0

The last non-zero remainder is 1, so GCF(27, 28) = 1.

LCM by listing multiples

Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, ...
Multiples of 28: 28, 56, 84, 112, 140, 168, 196, 224, 252, ...
The first number in both lists is 756.

Check: GCF × LCM = product

1 × 756 = 756 = 27 × 28. This always holds for two numbers, so you can find the LCM as (27 × 28) ÷ 1 = 756.

Simplifying the fraction 27/28

27/28 is already in lowest terms because the GCF of 27 and 28 is 1.

GCF and LCM of similar pairs

See also: factors of 27 · factors of 28.

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