GCF and LCM of 9 and 23

The GCF of 9 and 23 is 1. The LCM of 9 and 23 is 207.

9 and 23 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 9 × 23 = 207.

Method 1: list the factors (GCF)

Factors of 9: 1, 3, 9.
Factors of 23: 1, 23.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

9 = 3 × 3
23 = 23 (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 × 23 = 207.

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. 23 = 2 × 9 + 5
  2. 9 = 1 × 5 + 4
  3. 5 = 1 × 4 + 1
  4. 4 = 4 × 1 + 0

The last non-zero remainder is 1, so GCF(9, 23) = 1.

LCM by listing multiples

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, ...
Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, ...
The first number in both lists is 207.

Check: GCF × LCM = product

1 × 207 = 207 = 9 × 23. This always holds for two numbers, so you can find the LCM as (9 × 23) ÷ 1 = 207.

Simplifying the fraction 9/23

9/23 is already in lowest terms because the GCF of 9 and 23 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 23146
3 and 23169
4 and 23192
5 and 231115
6 and 231138
7 and 231161

See also: factors of 9 · factors of 23.

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