GCF and LCM of 10 and 13

The GCF of 10 and 13 is 1. The LCM of 10 and 13 is 130.

• GCF (greatest common factor, also called GCD or HCF) of 10 and 13 = 1
• LCM (least common multiple) of 10 and 13 = 130

10 and 13 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 10 × 13 = 130.

Method 1: list the factors (GCF)

Factors of 10: 1, 2, 5, 10.
Factors of 13: 1, 13.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

10 = 2 × 5
13 = 13 (prime)

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 × 5 × 13 = 130.

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. 13 = 1 × 10 + 3
2. 10 = 3 × 3 + 1
3. 3 = 3 × 1 + 0

The last non-zero remainder is 1, so GCF(10, 13) = 1.

LCM by listing multiples

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, ...
The first number in both lists is 130.

Check: GCF × LCM = product

1 × 130 = 130 = 10 × 13. This always holds for two numbers, so you can find the LCM as (10 × 13) ÷ 1 = 130.

Simplifying the fraction 10/13

10/13 is already in lowest terms because the GCF of 10 and 13 is 1.

GCF and LCM of similar pairs

See also: factors of 10 · factors of 13 · 10/13 as a decimal.

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