GCF and LCM of 9 and 13

The GCF of 9 and 13 is 1. The LCM of 9 and 13 is 117.

• GCF (greatest common factor, also called GCD or HCF) of 9 and 13 = 1
• LCM (least common multiple) of 9 and 13 = 117

9 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: 9 × 13 = 117.

Method 1: list the factors (GCF)

Factors of 9: 1, 3, 9.
Factors of 13: 1, 13.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

9 = 3 × 3
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: 3 × 3 × 13 = 117.

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 × 9 + 4
2. 9 = 2 × 4 + 1
3. 4 = 4 × 1 + 0

The last non-zero remainder is 1, so GCF(9, 13) = 1.

LCM by listing multiples

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, ...
Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, ...
The first number in both lists is 117.

Check: GCF × LCM = product

1 × 117 = 117 = 9 × 13. This always holds for two numbers, so you can find the LCM as (9 × 13) ÷ 1 = 117.

Simplifying the fraction 9/13

9/13 is already in lowest terms because the GCF of 9 and 13 is 1.

GCF and LCM of similar pairs

See also: factors of 9 · factors of 13 · 9/13 as a decimal.

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