GCF and LCM of 7 and 20

The GCF of 7 and 20 is 1. The LCM of 7 and 20 is 140.

7 and 20 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 7 × 20 = 140.

Method 1: list the factors (GCF)

Factors of 7: 1, 7.
Factors of 20: 1, 2, 4, 5, 10, 20.
Common factors: 1. The greatest of these is 1.

Method 2: prime factorization

7 = 7 (prime)
20 = 2 × 2 × 5

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 × 2 × 5 × 7 = 140.

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. 20 = 2 × 7 + 6
  2. 7 = 1 × 6 + 1
  3. 6 = 6 × 1 + 0

The last non-zero remainder is 1, so GCF(7, 20) = 1.

LCM by listing multiples

Multiples of 7: 7, 14, 21, 28, 35, 42, 49, 56, 63, ...
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, ...
The first number in both lists is 140.

Check: GCF × LCM = product

1 × 140 = 140 = 7 × 20. This always holds for two numbers, so you can find the LCM as (7 × 20) ÷ 1 = 140.

Simplifying the fraction 7/20

7/20 is already in lowest terms because the GCF of 7 and 20 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 20220
3 and 20160
4 and 20420
5 and 20520
6 and 20260
8 and 20440

See also: factors of 7 · factors of 20 · 7/20 as a decimal.

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