GCF and LCM of 11 and 21

The GCF of 11 and 21 is 1. The LCM of 11 and 21 is 231.

11 and 21 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 11 × 21 = 231.

Method 1: list the factors (GCF)

Factors of 11: 1, 11.
Factors of 21: 1, 3, 7, 21.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

11 = 11 (prime)
21 = 3 × 7

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 × 7 × 11 = 231.

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. 21 = 1 × 11 + 10
  2. 11 = 1 × 10 + 1
  3. 10 = 10 × 1 + 0

The last non-zero remainder is 1, so GCF(11, 21) = 1.

LCM by listing multiples

Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, 99, ...
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, ...
The first number in both lists is 231.

Check: GCF × LCM = product

1 × 231 = 231 = 11 × 21. This always holds for two numbers, so you can find the LCM as (11 × 21) ÷ 1 = 231.

Simplifying the fraction 11/21

11/21 is already in lowest terms because the GCF of 11 and 21 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 21142
3 and 21321
4 and 21184
5 and 211105
6 and 21342
7 and 21721

See also: factors of 11 · factors of 21.

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