GCF and LCM of 15 and 36

The GCF of 15 and 36 is 3. The LCM of 15 and 36 is 180.

• GCF (greatest common factor, also called GCD or HCF) of 15 and 36 = 3
• LCM (least common multiple) of 15 and 36 = 180

Method 1: list the factors (GCF)

Factors of 15: 1, 3, 5, 15.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Common factors: 1 and 3. The greatest of these is 3.

Method 2: prime factorization

15 = 3 × 5
36 = 2 × 2 × 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: 2 × 2 × 3 × 3 × 5 = 180.

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. 36 = 2 × 15 + 6
2. 15 = 2 × 6 + 3
3. 6 = 2 × 3 + 0

The last non-zero remainder is 3, so GCF(15, 36) = 3.

LCM by listing multiples

Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, ...
Multiples of 36: 36, 72, 108, 144, 180, 216, ...
The first number in both lists is 180.

Check: GCF × LCM = product

3 × 180 = 540 = 15 × 36. This always holds for two numbers, so you can find the LCM as (15 × 36) ÷ 3 = 180.

Simplifying the fraction 15/36

Divide the top and bottom by the GCF 3: 15/36 = 5/12.

GCF and LCM of similar pairs

See also: factors of 15 · factors of 36.

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