GCF and LCM of 18 and 50

The GCF of 18 and 50 is 2. The LCM of 18 and 50 is 450.

Method 1: list the factors (GCF)

Factors of 18: 1, 2, 3, 6, 9, 18.
Factors of 50: 1, 2, 5, 10, 25, 50.
Common factors: 1 and 2. The greatest of these is 2.

Method 2: prime factorization

18 = 2 × 3 × 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 × 3 × 3 × 5 × 5 = 450.

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 × 18 + 14
  2. 18 = 1 × 14 + 4
  3. 14 = 3 × 4 + 2
  4. 4 = 2 × 2 + 0

The last non-zero remainder is 2, so GCF(18, 50) = 2.

LCM by listing multiples

Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144, 162, ...
Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, ...
The first number in both lists is 450.

Check: GCF × LCM = product

2 × 450 = 900 = 18 × 50. This always holds for two numbers, so you can find the LCM as (18 × 50) ÷ 2 = 450.

Simplifying the fraction 18/50

Divide the top and bottom by the GCF 2: 18/50 = 9/25.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 18218
3 and 18318
4 and 18236
5 and 18190
6 and 18618
7 and 181126
2 and 50250
3 and 501150
4 and 502100
5 and 50550
6 and 502150
7 and 501350

See also: factors of 18 · factors of 50.

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