GCF and LCM of 5 and 12

The GCF of 5 and 12 is 1. The LCM of 5 and 12 is 60.

• GCF (greatest common factor, also called GCD or HCF) of 5 and 12 = 1
• LCM (least common multiple) of 5 and 12 = 60

5 and 12 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 5 × 12 = 60.

Method 1: list the factors (GCF)

Factors of 5: 1, 5.
Factors of 12: 1, 2, 3, 4, 6, 12.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

5 = 5 (prime)
12 = 2 × 2 × 3

GCF: multiply the prime factors both numbers share: there are none, so the GCF is 1.

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. 12 = 2 × 5 + 2
2. 5 = 2 × 2 + 1
3. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(5, 12) = 1.

LCM by listing multiples

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, ...
Multiples of 12: 12, 24, 36, 48, 60, 72, ...
The first number in both lists is 60.

Check: GCF × LCM = product

1 × 60 = 60 = 5 × 12. This always holds for two numbers, so you can find the LCM as (5 × 12) ÷ 1 = 60.

Simplifying the fraction 5/12

5/12 is already in lowest terms because the GCF of 5 and 12 is 1.

GCF and LCM of similar pairs

See also: factors of 5 · factors of 12 · 5/12 as a decimal.

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