GCF and LCM of 24 and 100

The GCF of 24 and 100 is 4. The LCM of 24 and 100 is 600.

• GCF (greatest common factor, also called GCD or HCF) of 24 and 100 = 4
• LCM (least common multiple) of 24 and 100 = 600

Method 1: list the factors (GCF)

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1, 2 and 4. The greatest of these is 4.

Method 2: prime factorization

24 = 2 × 2 × 2 × 3
100 = 2 × 2 × 5 × 5

GCF: multiply the prime factors both numbers share: 2 × 2 = 4.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 3 × 5 × 5 = 600.

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. 100 = 4 × 24 + 4
2. 24 = 6 × 4 + 0

The last non-zero remainder is 4, so GCF(24, 100) = 4.

LCM by listing multiples

Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, ...
Multiples of 100: 100, 200, 300, 400, 500, 600, 700, ...
The first number in both lists is 600.

Check: GCF × LCM = product

4 × 600 = 2,400 = 24 × 100. This always holds for two numbers, so you can find the LCM as (24 × 100) ÷ 4 = 600.

Simplifying the fraction 24/100

Divide the top and bottom by the GCF 4: 24/100 = 6/25.

GCF and LCM of similar pairs

See also: factors of 24 · factors of 100.

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