GCF and LCM of 13 and 45

The GCF of 13 and 45 is 1. The LCM of 13 and 45 is 585.

• GCF (greatest common factor, also called GCD or HCF) of 13 and 45 = 1
• LCM (least common multiple) of 13 and 45 = 585

13 and 45 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 13 × 45 = 585.

Method 1: list the factors (GCF)

Factors of 13: 1, 13.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

13 = 13 (prime)
45 = 3 × 3 × 5

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 × 5 × 13 = 585.

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. 45 = 3 × 13 + 6
2. 13 = 2 × 6 + 1
3. 6 = 6 × 1 + 0

The last non-zero remainder is 1, so GCF(13, 45) = 1.

LCM by listing multiples

Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, ...
Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...
The first number in both lists is 585.

Check: GCF × LCM = product

1 × 585 = 585 = 13 × 45. This always holds for two numbers, so you can find the LCM as (13 × 45) ÷ 1 = 585.

Simplifying the fraction 13/45

13/45 is already in lowest terms because the GCF of 13 and 45 is 1.

GCF and LCM of similar pairs

See also: factors of 13 · factors of 45.

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