GCF and LCM of 9 and 100

The GCF of 9 and 100 is 1. The LCM of 9 and 100 is 900.

• GCF (greatest common factor, also called GCD or HCF) of 9 and 100 = 1
• LCM (least common multiple) of 9 and 100 = 900

9 and 100 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 9 × 100 = 900.

Method 1: list the factors (GCF)

Factors of 9: 1, 3, 9.
Factors of 100: 1, 2, 4, 5, 10, 20, 25, 50, 100.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

9 = 3 × 3
100 = 2 × 2 × 5 × 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: 2 × 2 × 3 × 3 × 5 × 5 = 900.

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. 100 = 11 × 9 + 1
2. 9 = 9 × 1 + 0

The last non-zero remainder is 1, so GCF(9, 100) = 1.

LCM by listing multiples

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, ...
Multiples of 100: 100, 200, 300, 400, 500, 600, 700, 800, 900, ...
The first number in both lists is 900.

Check: GCF × LCM = product

1 × 900 = 900 = 9 × 100. This always holds for two numbers, so you can find the LCM as (9 × 100) ÷ 1 = 900.

Simplifying the fraction 9/100

9/100 is already in lowest terms because the GCF of 9 and 100 is 1.

GCF and LCM of similar pairs

See also: factors of 9 · factors of 100.

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