GCF and LCM of 7 and 27

The GCF of 7 and 27 is 1. The LCM of 7 and 27 is 189.

• GCF (greatest common factor, also called GCD or HCF) of 7 and 27 = 1
• LCM (least common multiple) of 7 and 27 = 189

7 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: 7 × 27 = 189.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

7 = 7 (prime)
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: 3 × 3 × 3 × 7 = 189.

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 × 7 + 6
2. 7 = 1 × 6 + 1
3. 6 = 6 × 1 + 0

The last non-zero remainder is 1, so GCF(7, 27) = 1.

LCM by listing multiples

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, ...
Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, ...
The first number in both lists is 189.

Check: GCF × LCM = product

1 × 189 = 189 = 7 × 27. This always holds for two numbers, so you can find the LCM as (7 × 27) ÷ 1 = 189.

Simplifying the fraction 7/27

7/27 is already in lowest terms because the GCF of 7 and 27 is 1.

GCF and LCM of similar pairs

See also: factors of 7 · factors of 27.

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