GCF and LCM of 24 and 27

The GCF of 24 and 27 is 3. The LCM of 24 and 27 is 216.

• GCF (greatest common factor, also called GCD or HCF) of 24 and 27 = 3
• LCM (least common multiple) of 24 and 27 = 216

Method 1: list the factors (GCF)

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Factors of 27: 1, 3, 9, 27.
Common factors: 1 and 3. The greatest of these is 3.

Method 2: prime factorization

24 = 2 × 2 × 2 × 3
27 = 3 × 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 × 2 × 3 × 3 × 3 = 216.

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. 27 = 1 × 24 + 3
2. 24 = 8 × 3 + 0

The last non-zero remainder is 3, so GCF(24, 27) = 3.

LCM by listing multiples

Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, ...
Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, ...
The first number in both lists is 216.

Check: GCF × LCM = product

3 × 216 = 648 = 24 × 27. This always holds for two numbers, so you can find the LCM as (24 × 27) ÷ 3 = 216.

Simplifying the fraction 24/27

Divide the top and bottom by the GCF 3: 24/27 = 8/9.

GCF and LCM of similar pairs

See also: factors of 24 · factors of 27.

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