GCF and LCM of 36 and 40

The GCF of 36 and 40 is 4. The LCM of 36 and 40 is 360.

• GCF (greatest common factor, also called GCD or HCF) of 36 and 40 = 4
• LCM (least common multiple) of 36 and 40 = 360

Method 1: list the factors (GCF)

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Common factors: 1, 2 and 4. The greatest of these is 4.

Method 2: prime factorization

36 = 2 × 2 × 3 × 3
40 = 2 × 2 × 2 × 5

GCF: multiply the prime factors both numbers share: 2 × 2 = 4.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 3 × 3 × 5 = 360.

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. 40 = 1 × 36 + 4
2. 36 = 9 × 4 + 0

The last non-zero remainder is 4, so GCF(36, 40) = 4.

LCM by listing multiples

Multiples of 36: 36, 72, 108, 144, 180, 216, 252, 288, 324, ...
Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, ...
The first number in both lists is 360.

Check: GCF × LCM = product

4 × 360 = 1,440 = 36 × 40. This always holds for two numbers, so you can find the LCM as (36 × 40) ÷ 4 = 360.

Simplifying the fraction 36/40

Divide the top and bottom by the GCF 4: 36/40 = 9/10.

GCF and LCM of similar pairs

See also: factors of 36 · factors of 40.

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