GCF and LCM of 40 and 100

The GCF of 40 and 100 is 20. The LCM of 40 and 100 is 200.

Method 1: list the factors (GCF)

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1, 2, 4, 5, 10 and 20. The greatest of these is 20.

Method 2: prime factorization

40 = 2 × 2 × 2 × 5
100 = 2 × 2 × 5 × 5

GCF: multiply the prime factors both numbers share: 2 × 2 × 5 = 20.

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. 100 = 2 × 40 + 20
  2. 40 = 2 × 20 + 0

The last non-zero remainder is 20, so GCF(40, 100) = 20.

LCM by listing multiples

Multiples of 40: 40, 80, 120, 160, 200, 240, ...
Multiples of 100: 100, 200, 300, ...
The first number in both lists is 200.

Check: GCF × LCM = product

20 × 200 = 4,000 = 40 × 100. This always holds for two numbers, so you can find the LCM as (40 × 100) ÷ 20 = 200.

Simplifying the fraction 40/100

Divide the top and bottom by the GCF 20: 40/100 = 2/5.

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 1002100
3 and 1001300
4 and 1004100
5 and 1005100
6 and 1002300
7 and 1001700

See also: factors of 40 · factors of 100.

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