GCF and LCM of 36 and 48

The GCF of 36 and 48 is 12. The LCM of 36 and 48 is 144.

• GCF (greatest common factor, also called GCD or HCF) of 36 and 48 = 12
• LCM (least common multiple) of 36 and 48 = 144

Method 1: list the factors (GCF)

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Common factors: 1, 2, 3, 4, 6 and 12. The greatest of these is 12.

Method 2: prime factorization

36 = 2 × 2 × 3 × 3
48 = 2 × 2 × 2 × 2 × 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 × 2 × 3 × 3 = 144.

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. 48 = 1 × 36 + 12
2. 36 = 3 × 12 + 0

The last non-zero remainder is 12, so GCF(36, 48) = 12.

LCM by listing multiples

Multiples of 36: 36, 72, 108, 144, 180, ...
Multiples of 48: 48, 96, 144, 192, ...
The first number in both lists is 144.

Check: GCF × LCM = product

12 × 144 = 1,728 = 36 × 48. This always holds for two numbers, so you can find the LCM as (36 × 48) ÷ 12 = 144.

Simplifying the fraction 36/48

Divide the top and bottom by the GCF 12: 36/48 = 3/4.

GCF and LCM of similar pairs

See also: factors of 36 · factors of 48.

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