What is the GCF of 45 and 60?

The greatest common factor of 45 and 60 is 15.

What is the LCM of 45 and 60?

The least common multiple of 45 and 60 is 180.

Are 45 and 60 coprime?

No. They share the common factors 3, 5 and 15, and their GCF is 15.

GCF and LCM of 45 and 60

The GCF of 45 and 60 is 15. The LCM of 45 and 60 is 180.

GCF (greatest common factor, also called GCD or HCF) of 45 and 60 = 15
LCM (least common multiple) of 45 and 60 = 180

Method 1: list the factors (GCF)

Factors of 45: 1, 3, 5, 9, 15, 45.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors: 1, 3, 5 and 15. The greatest of these is 15.

Method 2: prime factorization

45 = 3 × 3 × 5
60 = 2 × 2 × 3 × 5

GCF: multiply the prime factors both numbers share: 3 × 5 = 15.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 3 × 5 = 180.

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.

60 = 1 × 45 + 15
45 = 3 × 15 + 0

The last non-zero remainder is 15, so GCF(45, 60) = 15.

LCM by listing multiples

Multiples of 45: 45, 90, 135, 180, 225, ...
Multiples of 60: 60, 120, 180, 240, ...
The first number in both lists is 180.

Check: GCF × LCM = product

15 × 180 = 2,700 = 45 × 60. This always holds for two numbers, so you can find the LCM as (45 × 60) ÷ 15 = 180.

Simplifying the fraction 45/60

Divide the top and bottom by the GCF 15: 45/60 = 3/4.

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 60	2	60
3 and 60	3	60
4 and 60	4	60
5 and 60	5	60
6 and 60	6	60
7 and 60	1	420

See also: factors of 45 · factors of 60.

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