What is the GCF of 27 and 60?

The greatest common factor of 27 and 60 is 3.

What is the LCM of 27 and 60?

The least common multiple of 27 and 60 is 540.

Are 27 and 60 coprime?

No. They share the common factor 3, and their GCF is 3.

GCF and LCM of 27 and 60

The GCF of 27 and 60 is 3. The LCM of 27 and 60 is 540.

GCF (greatest common factor, also called GCD or HCF) of 27 and 60 = 3
LCM (least common multiple) of 27 and 60 = 540

Method 1: list the factors (GCF)

Factors of 27: 1, 3, 9, 27.
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
Common factors: 1 and 3. The greatest of these is 3.

Method 2: prime factorization

27 = 3 × 3 × 3
60 = 2 × 2 × 3 × 5

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

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 3 × 3 × 5 = 540.

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 = 2 × 27 + 6
27 = 4 × 6 + 3
6 = 2 × 3 + 0

The last non-zero remainder is 3, so GCF(27, 60) = 3.

LCM by listing multiples

Multiples of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, ...
Multiples of 60: 60, 120, 180, 240, 300, 360, 420, 480, 540, ...
The first number in both lists is 540.

Check: GCF × LCM = product

3 × 540 = 1,620 = 27 × 60. This always holds for two numbers, so you can find the LCM as (27 × 60) ÷ 3 = 540.

Simplifying the fraction 27/60

Divide the top and bottom by the GCF 3: 27/60 = 9/20.

GCF and LCM of similar pairs

Numbers	GCF	LCM
2 and 27	1	54
3 and 27	3	27
4 and 27	1	108
5 and 27	1	135
6 and 27	3	54
7 and 27	1	189
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 27 · factors of 60.

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