GCF and LCM of 24 and 48

The GCF of 24 and 48 is 24. The LCM of 24 and 48 is 48.

• GCF (greatest common factor, also called GCD or HCF) of 24 and 48 = 24
• LCM (least common multiple) of 24 and 48 = 48

Method 1: list the factors (GCF)

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

Method 2: prime factorization

24 = 2 × 2 × 2 × 3
48 = 2 × 2 × 2 × 2 × 3

GCF: multiply the prime factors both numbers share: 2 × 2 × 2 × 3 = 24.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 2 × 3 = 48.

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 = 2 × 24 + 0

The last non-zero remainder is 24, so GCF(24, 48) = 24.

LCM by listing multiples

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

Check: GCF × LCM = product

24 × 48 = 1,152 = 24 × 48. This always holds for two numbers, so you can find the LCM as (24 × 48) ÷ 24 = 48.

Simplifying the fraction 24/48

Divide the top and bottom by the GCF 24: 24/48 = 1/2.

GCF and LCM of similar pairs

See also: factors of 24 · factors of 48.

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