GCF and LCM of 40 and 50

The GCF of 40 and 50 is 10. The LCM of 40 and 50 is 200.

Method 1: list the factors (GCF)

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Factors of 50: 1, 2, 5, 10, 25, 50.
Common factors: 1, 2, 5 and 10. The greatest of these is 10.

Method 2: prime factorization

40 = 2 × 2 × 2 × 5
50 = 2 × 5 × 5

GCF: multiply the prime factors both numbers share: 2 × 5 = 10.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 5 × 5 = 200.

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 = 1 × 40 + 10
  2. 40 = 4 × 10 + 0

The last non-zero remainder is 10, so GCF(40, 50) = 10.

LCM by listing multiples

Multiples of 40: 40, 80, 120, 160, 200, 240, ...
Multiples of 50: 50, 100, 150, 200, 250, ...
The first number in both lists is 200.

Check: GCF × LCM = product

10 × 200 = 2,000 = 40 × 50. This always holds for two numbers, so you can find the LCM as (40 × 50) ÷ 10 = 200.

Simplifying the fraction 40/50

Divide the top and bottom by the GCF 10: 40/50 = 4/5.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 40240
3 and 401120
4 and 40440
5 and 40540
6 and 402120
7 and 401280
2 and 50250
3 and 501150
4 and 502100
5 and 50550
6 and 502150
7 and 501350

See also: factors of 40 · factors of 50.

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