What is the GCF of 45 and 100?

The greatest common factor of 45 and 100 is 5.

What is the LCM of 45 and 100?

The least common multiple of 45 and 100 is 900.

Are 45 and 100 coprime?

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

GCF and LCM of 45 and 100

The GCF of 45 and 100 is 5. The LCM of 45 and 100 is 900.

GCF (greatest common factor, also called GCD or HCF) of 45 and 100 = 5
LCM (least common multiple) of 45 and 100 = 900

Method 1: list the factors (GCF)

Factors of 45: 1, 3, 5, 9, 15, 45.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1 and 5. The greatest of these is 5.

Method 2: prime factorization

45 = 3 × 3 × 5
100 = 2 × 2 × 5 × 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 × 3 × 3 × 5 × 5 = 900.

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.

100 = 2 × 45 + 10
45 = 4 × 10 + 5
10 = 2 × 5 + 0

The last non-zero remainder is 5, so GCF(45, 100) = 5.

LCM by listing multiples

Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...
Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, ...
The first number in both lists is 900.

Check: GCF × LCM = product

5 × 900 = 4,500 = 45 × 100. This always holds for two numbers, so you can find the LCM as (45 × 100) ÷ 5 = 900.

Simplifying the fraction 45/100

Divide the top and bottom by the GCF 5: 45/100 = 9/20.

GCF and LCM of similar pairs

Numbers	GCF	LCM
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
2 and 100	2	100
3 and 100	1	300
4 and 100	4	100
5 and 100	5	100
6 and 100	2	300
7 and 100	1	700

See also: factors of 45 · factors of 100.

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