GCF and LCM of 27 and 50

The GCF of 27 and 50 is 1. The LCM of 27 and 50 is 1,350.

• GCF (greatest common factor, also called GCD or HCF) of 27 and 50 = 1
• LCM (least common multiple) of 27 and 50 = 1,350

27 and 50 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 27 × 50 = 1,350.

Method 1: list the factors (GCF)

Factors of 27: 1, 3, 9, 27.
Factors of 50: 1, 2, 5, 10, 25, 50.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

27 = 3 × 3 × 3
50 = 2 × 5 × 5

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 × 3 × 3 × 3 × 5 × 5 = 1,350.

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. 50 = 1 × 27 + 23
2. 27 = 1 × 23 + 4
3. 23 = 5 × 4 + 3
4. 4 = 1 × 3 + 1
5. 3 = 3 × 1 + 0

The last non-zero remainder is 1, so GCF(27, 50) = 1.

LCM by listing multiples

Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, ...
Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, ...
The first number in both lists is 1,350.

Check: GCF × LCM = product

1 × 1,350 = 1,350 = 27 × 50. This always holds for two numbers, so you can find the LCM as (27 × 50) ÷ 1 = 1,350.

Simplifying the fraction 27/50

27/50 is already in lowest terms because the GCF of 27 and 50 is 1.

GCF and LCM of similar pairs

See also: factors of 27 · factors of 50 · 27/50 as a decimal.

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