GCF and LCM of 9 and 16

The GCF of 9 and 16 is 1. The LCM of 9 and 16 is 144.

• GCF (greatest common factor, also called GCD or HCF) of 9 and 16 = 1
• LCM (least common multiple) of 9 and 16 = 144

9 and 16 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 9 × 16 = 144.

Method 1: list the factors (GCF)

Factors of 9: 1, 3, 9.
Factors of 16: 1, 2, 4, 8, 16.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

9 = 3 × 3
16 = 2 × 2 × 2 × 2

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 × 2 × 2 × 2 × 3 × 3 = 144.

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. 16 = 1 × 9 + 7
2. 9 = 1 × 7 + 2
3. 7 = 3 × 2 + 1
4. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(9, 16) = 1.

LCM by listing multiples

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, ...
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144, ...
The first number in both lists is 144.

Check: GCF × LCM = product

1 × 144 = 144 = 9 × 16. This always holds for two numbers, so you can find the LCM as (9 × 16) ÷ 1 = 144.

Simplifying the fraction 9/16

9/16 is already in lowest terms because the GCF of 9 and 16 is 1.

GCF and LCM of similar pairs

See also: factors of 9 · factors of 16 · 9/16 as a decimal.

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