GCF and LCM of 9 and 17

The GCF of 9 and 17 is 1. The LCM of 9 and 17 is 153.

• GCF (greatest common factor, also called GCD or HCF) of 9 and 17 = 1
• LCM (least common multiple) of 9 and 17 = 153

9 and 17 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 9 × 17 = 153.

Method 1: list the factors (GCF)

Factors of 9: 1, 3, 9.
Factors of 17: 1, 17.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

9 = 3 × 3
17 = 17 (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 × 17 = 153.

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. 17 = 1 × 9 + 8
2. 9 = 1 × 8 + 1
3. 8 = 8 × 1 + 0

The last non-zero remainder is 1, so GCF(9, 17) = 1.

LCM by listing multiples

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, ...
Multiples of 17: 17, 34, 51, 68, 85, 102, 119, 136, 153, ...
The first number in both lists is 153.

Check: GCF × LCM = product

1 × 153 = 153 = 9 × 17. This always holds for two numbers, so you can find the LCM as (9 × 17) ÷ 1 = 153.

Simplifying the fraction 9/17

9/17 is already in lowest terms because the GCF of 9 and 17 is 1.

GCF and LCM of similar pairs

See also: factors of 9 · factors of 17 · 9/17 as a decimal.

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