GCF and LCM of 9 and 50

The GCF of 9 and 50 is 1. The LCM of 9 and 50 is 450.

9 and 50 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 9 × 50 = 450.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

9 = 3 × 3
50 = 2 × 5 × 5

GCF: multiply the prime factors both numbers share: there are none, so the GCF is 1.

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 = 5 × 9 + 5
  2. 9 = 1 × 5 + 4
  3. 5 = 1 × 4 + 1
  4. 4 = 4 × 1 + 0

The last non-zero remainder is 1, so GCF(9, 50) = 1.

LCM by listing multiples

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, ...
Multiples of 50: 50, 100, 150, 200, 250, 300, 350, 400, 450, ...
The first number in both lists is 450.

Check: GCF × LCM = product

1 × 450 = 450 = 9 × 50. This always holds for two numbers, so you can find the LCM as (9 × 50) ÷ 1 = 450.

Simplifying the fraction 9/50

9/50 is already in lowest terms because the GCF of 9 and 50 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 9118
3 and 939
4 and 9136
5 and 9145
6 and 9318
7 and 9163
2 and 50250
3 and 501150
4 and 502100
5 and 50550
6 and 502150
7 and 501350

See also: factors of 9 · factors of 50 · 9/50 as a decimal.

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