The GCF of 20 and 21 is 1. The LCM of 20 and 21 is 420.
20 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: 20 × 21 = 420.
Factors of 20: 1, 2, 4, 5, 10, 20.
Factors of 21: 1, 3, 7, 21.
Common factors: 1. The greatest of these is 1.
20 = 2 × 2 × 5
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: 2 × 2 × 3 × 5 × 7 = 420.
Divide the larger number by the smaller and repeat with the remainder until it is 0. The last non-zero remainder is the GCF.
The last non-zero remainder is 1, so GCF(20, 21) = 1.
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, ...
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, ...
The first number in both lists is 420.
1 × 420 = 420 = 20 × 21. This always holds for two numbers, so you can find the LCM as (20 × 21) ÷ 1 = 420.
20/21 is already in lowest terms because the GCF of 20 and 21 is 1.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 20 | 2 | 20 |
| 3 and 20 | 1 | 60 |
| 4 and 20 | 4 | 20 |
| 5 and 20 | 5 | 20 |
| 6 and 20 | 2 | 60 |
| 7 and 20 | 1 | 140 |
| 2 and 21 | 1 | 42 |
| 3 and 21 | 3 | 21 |
| 4 and 21 | 1 | 84 |
| 5 and 21 | 1 | 105 |
| 6 and 21 | 3 | 42 |
| 7 and 21 | 7 | 21 |
See also: factors of 20 · factors of 21.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.