GCF and LCM of 13 and 22

The GCF of 13 and 22 is 1. The LCM of 13 and 22 is 286.

13 and 22 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 13 × 22 = 286.

Method 1: list the factors (GCF)

Factors of 13: 1, 13.
Factors of 22: 1, 2, 11, 22.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

13 = 13 (prime)
22 = 2 × 11

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 × 11 × 13 = 286.

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. 22 = 1 × 13 + 9
  2. 13 = 1 × 9 + 4
  3. 9 = 2 × 4 + 1
  4. 4 = 4 × 1 + 0

The last non-zero remainder is 1, so GCF(13, 22) = 1.

LCM by listing multiples

Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, ...
Multiples of 22: 22, 44, 66, 88, 110, 132, 154, 176, 198, ...
The first number in both lists is 286.

Check: GCF × LCM = product

1 × 286 = 286 = 13 × 22. This always holds for two numbers, so you can find the LCM as (13 × 22) ÷ 1 = 286.

Simplifying the fraction 13/22

13/22 is already in lowest terms because the GCF of 13 and 22 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 13126
3 and 13139
4 and 13152
5 and 13165
6 and 13178
7 and 13191
2 and 22222
3 and 22166
4 and 22244
5 and 221110
6 and 22266
7 and 221154

See also: factors of 13 · factors of 22.

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