GCF and LCM of 24 and 60

The GCF of 24 and 60 is 12. The LCM of 24 and 60 is 120.

• GCF (greatest common factor, also called GCD or HCF) of 24 and 60 = 12
• LCM (least common multiple) of 24 and 60 = 120

Method 1: list the factors (GCF)

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors: 1, 2, 3, 4, 6 and 12. The greatest of these is 12.

Method 2: prime factorization

24 = 2 × 2 × 2 × 3
60 = 2 × 2 × 3 × 5

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 × 5 = 120.

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. 60 = 2 × 24 + 12
2. 24 = 2 × 12 + 0

The last non-zero remainder is 12, so GCF(24, 60) = 12.

LCM by listing multiples

Multiples of 24: 24, 48, 72, 96, 120, 144, ...
Multiples of 60: 60, 120, 180, ...
The first number in both lists is 120.

Check: GCF × LCM = product

12 × 120 = 1,440 = 24 × 60. This always holds for two numbers, so you can find the LCM as (24 × 60) ÷ 12 = 120.

Simplifying the fraction 24/60

Divide the top and bottom by the GCF 12: 24/60 = 2/5.

GCF and LCM of similar pairs

See also: factors of 24 · factors of 60.

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