GCF and LCM of 24 and 50

The GCF of 24 and 50 is 2. The LCM of 24 and 50 is 600.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

24 = 2 × 2 × 2 × 3
50 = 2 × 5 × 5

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

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. 50 = 2 × 24 + 2
  2. 24 = 12 × 2 + 0

The last non-zero remainder is 2, so GCF(24, 50) = 2.

LCM by listing multiples

Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, ...
Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, ...
The first number in both lists is 600.

Check: GCF × LCM = product

2 × 600 = 1,200 = 24 × 50. This always holds for two numbers, so you can find the LCM as (24 × 50) ÷ 2 = 600.

Simplifying the fraction 24/50

Divide the top and bottom by the GCF 2: 24/50 = 12/25.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 24224
3 and 24324
4 and 24424
5 and 241120
6 and 24624
7 and 241168
2 and 50250
3 and 501150
4 and 502100
5 and 50550
6 and 502150
7 and 501350

See also: factors of 24 · factors of 50.

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