GCF and LCM of 9 and 11

The GCF of 9 and 11 is 1. The LCM of 9 and 11 is 99.

9 and 11 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 9 × 11 = 99.

Method 1: list the factors (GCF)

Factors of 9: 1, 3, 9.
Factors of 11: 1, 11.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

9 = 3 × 3
11 = 11 (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 × 11 = 99.

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. 11 = 1 × 9 + 2
  2. 9 = 4 × 2 + 1
  3. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(9, 11) = 1.

LCM by listing multiples

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, ...
Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, ...
The first number in both lists is 99.

Check: GCF × LCM = product

1 × 99 = 99 = 9 × 11. This always holds for two numbers, so you can find the LCM as (9 × 11) ÷ 1 = 99.

Simplifying the fraction 9/11

9/11 is already in lowest terms because the GCF of 9 and 11 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 9118
3 and 939
4 and 9136
5 and 9145
6 and 9318
7 and 9163
2 and 11122
3 and 11133
4 and 11144
5 and 11155
6 and 11166
7 and 11177

See also: factors of 9 · factors of 11 · 9/11 as a decimal.

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