What is the GCF of 40 and 45?

The greatest common factor of 40 and 45 is 5.

What is the LCM of 40 and 45?

The least common multiple of 40 and 45 is 360.

Are 40 and 45 coprime?

No. They share the common factor 5, and their GCF is 5.

GCF and LCM of 40 and 45

The GCF of 40 and 45 is 5. The LCM of 40 and 45 is 360.

GCF (greatest common factor, also called GCD or HCF) of 40 and 45 = 5
LCM (least common multiple) of 40 and 45 = 360

Method 1: list the factors (GCF)

Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1 and 5. The greatest of these is 5.

Method 2: prime factorization

40 = 2 × 2 × 2 × 5
45 = 3 × 3 × 5

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

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.

45 = 1 × 40 + 5
40 = 8 × 5 + 0

The last non-zero remainder is 5, so GCF(40, 45) = 5.

LCM by listing multiples

Multiples of 40: 40, 80, 120, 160, 200, 240, 280, 320, 360, ...
Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...
The first number in both lists is 360.

Check: GCF × LCM = product

5 × 360 = 1,800 = 40 × 45. This always holds for two numbers, so you can find the LCM as (40 × 45) ÷ 5 = 360.

Simplifying the fraction 40/45

Divide the top and bottom by the GCF 5: 40/45 = 8/9.

GCF and LCM of similar pairs

Numbers	GCF	LCM
2 and 40	2	40
3 and 40	1	120
4 and 40	4	40
5 and 40	5	40
6 and 40	2	120
7 and 40	1	280
2 and 45	1	90
3 and 45	3	45
4 and 45	1	180
5 and 45	5	45
6 and 45	3	90
7 and 45	1	315

See also: factors of 40 · factors of 45.

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