GCF and LCM of 5 and 9

The GCF of 5 and 9 is 1. The LCM of 5 and 9 is 45.

• GCF (greatest common factor, also called GCD or HCF) of 5 and 9 = 1
• LCM (least common multiple) of 5 and 9 = 45

5 and 9 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 5 × 9 = 45.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

5 = 5 (prime)
9 = 3 × 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: 3 × 3 × 5 = 45.

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. 9 = 1 × 5 + 4
2. 5 = 1 × 4 + 1
3. 4 = 4 × 1 + 0

The last non-zero remainder is 1, so GCF(5, 9) = 1.

LCM by listing multiples

Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, ...
Multiples of 9: 9, 18, 27, 36, 45, 54, ...
The first number in both lists is 45.

Check: GCF × LCM = product

1 × 45 = 45 = 5 × 9. This always holds for two numbers, so you can find the LCM as (5 × 9) ÷ 1 = 45.

Simplifying the fraction 5/9

5/9 is already in lowest terms because the GCF of 5 and 9 is 1.

GCF and LCM of similar pairs

See also: factors of 5 · factors of 9 · 5/9 as a decimal.

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