GCF and LCM of 24 and 36

The GCF of 24 and 36 is 12. The LCM of 24 and 36 is 72.

• GCF (greatest common factor, also called GCD or HCF) of 24 and 36 = 12
• LCM (least common multiple) of 24 and 36 = 72

Method 1: list the factors (GCF)

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Common factors: 1, 2, 3, 4, 6 and 12. The greatest of these is 12.

Method 2: prime factorization

24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3

GCF: multiply the prime factors both numbers share: 2 × 2 × 3 = 12.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 3 × 3 = 72.

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 = 1 × 24 + 12
2. 24 = 2 × 12 + 0

The last non-zero remainder is 12, so GCF(24, 36) = 12.

LCM by listing multiples

Multiples of 24: 24, 48, 72, 96, ...
Multiples of 36: 36, 72, 108, ...
The first number in both lists is 72.

Check: GCF × LCM = product

12 × 72 = 864 = 24 × 36. This always holds for two numbers, so you can find the LCM as (24 × 36) ÷ 12 = 72.

Simplifying the fraction 24/36

Divide the top and bottom by the GCF 12: 24/36 = 2/3.

GCF and LCM of similar pairs

See also: factors of 24 · factors of 36.

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