GCF and LCM of 11 and 13

The GCF of 11 and 13 is 1. The LCM of 11 and 13 is 143.

11 and 13 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 11 × 13 = 143.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

11 = 11 (prime)
13 = 13 (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: 11 × 13 = 143.

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. 13 = 1 × 11 + 2
  2. 11 = 5 × 2 + 1
  3. 2 = 2 × 1 + 0

The last non-zero remainder is 1, so GCF(11, 13) = 1.

LCM by listing multiples

Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, ...
Multiples of 13: 13, 26, 39, 52, 65, 78, 91, 104, 117, ...
The first number in both lists is 143.

Check: GCF × LCM = product

1 × 143 = 143 = 11 × 13. This always holds for two numbers, so you can find the LCM as (11 × 13) ÷ 1 = 143.

Simplifying the fraction 11/13

11/13 is already in lowest terms because the GCF of 11 and 13 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 11122
3 and 11133
4 and 11144
5 and 11155
6 and 11166
7 and 11177
2 and 13126
3 and 13139
4 and 13152
5 and 13165
6 and 13178
7 and 13191

See also: factors of 11 · factors of 13 · 11/13 as a decimal.

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