GCF and LCM of 15 and 27

The GCF of 15 and 27 is 3. The LCM of 15 and 27 is 135.

• GCF (greatest common factor, also called GCD or HCF) of 15 and 27 = 3
• LCM (least common multiple) of 15 and 27 = 135

Method 1: list the factors (GCF)

Factors of 15: 1, 3, 5, 15.
Factors of 27: 1, 3, 9, 27.
Common factors: 1 and 3. The greatest of these is 3.

Method 2: prime factorization

15 = 3 × 5
27 = 3 × 3 × 3

GCF: multiply the prime factors both numbers share: 3 = 3.

LCM: multiply every prime the maximum number of times it appears in either number: 3 × 3 × 3 × 5 = 135.

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 = 1 × 15 + 12
2. 15 = 1 × 12 + 3
3. 12 = 4 × 3 + 0

The last non-zero remainder is 3, so GCF(15, 27) = 3.

LCM by listing multiples

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, ...
Multiples of 27: 27, 54, 81, 108, 135, 162, ...
The first number in both lists is 135.

Check: GCF × LCM = product

3 × 135 = 405 = 15 × 27. This always holds for two numbers, so you can find the LCM as (15 × 27) ÷ 3 = 135.

Simplifying the fraction 15/27

Divide the top and bottom by the GCF 3: 15/27 = 5/9.

GCF and LCM of similar pairs

See also: factors of 15 · factors of 27.

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