GCF and LCM of 30 and 60

The GCF of 30 and 60 is 30. The LCM of 30 and 60 is 60.

• GCF (greatest common factor, also called GCD or HCF) of 30 and 60 = 30
• LCM (least common multiple) of 30 and 60 = 60

Method 1: list the factors (GCF)

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

Method 2: prime factorization

30 = 2 × 3 × 5
60 = 2 × 2 × 3 × 5

GCF: multiply the prime factors both numbers share: 2 × 3 × 5 = 30.

LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 5 = 60.

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. 60 = 2 × 30 + 0

The last non-zero remainder is 30, so GCF(30, 60) = 30.

LCM by listing multiples

Multiples of 30: 30, 60, 90, ...
Multiples of 60: 60, 120, ...
The first number in both lists is 60.

Check: GCF × LCM = product

30 × 60 = 1,800 = 30 × 60. This always holds for two numbers, so you can find the LCM as (30 × 60) ÷ 30 = 60.

Simplifying the fraction 30/60

Divide the top and bottom by the GCF 30: 30/60 = 1/2.

GCF and LCM of similar pairs

See also: factors of 30 · factors of 60.

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