GCF and LCM of 7 and 11

The GCF of 7 and 11 is 1. The LCM of 7 and 11 is 77.

7 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: 7 × 11 = 77.

Method 1: list the factors (GCF)

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

Method 2: prime factorization

7 = 7 (prime)
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: 7 × 11 = 77.

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 × 7 + 4
  2. 7 = 1 × 4 + 3
  3. 4 = 1 × 3 + 1
  4. 3 = 3 × 1 + 0

The last non-zero remainder is 1, so GCF(7, 11) = 1.

LCM by listing multiples

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, ...
Multiples of 11: 11, 22, 33, 44, 55, 66, 77, 88, ...
The first number in both lists is 77.

Check: GCF × LCM = product

1 × 77 = 77 = 7 × 11. This always holds for two numbers, so you can find the LCM as (7 × 11) ÷ 1 = 77.

Simplifying the fraction 7/11

7/11 is already in lowest terms because the GCF of 7 and 11 is 1.

GCF and LCM of similar pairs

NumbersGCFLCM
2 and 7114
3 and 7121
4 and 7128
5 and 7135
6 and 7142
7 and 8156
2 and 11122
3 and 11133
4 and 11144
5 and 11155
6 and 11166
8 and 11188

See also: factors of 7 · factors of 11 · 7/11 as a decimal.

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