The GCF of 5 and 21 is 1. The LCM of 5 and 21 is 105.
5 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: 5 × 21 = 105.
Factors of 5: 1, 5.
Factors of 21: 1, 3, 7, 21.
Common factors: 1. The greatest of these is 1.
5 = 5 (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 × 5 × 7 = 105.
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(5, 21) = 1.
Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, ...
Multiples of 21: 21, 42, 63, 84, 105, 126, ...
The first number in both lists is 105.
1 × 105 = 105 = 5 × 21. This always holds for two numbers, so you can find the LCM as (5 × 21) ÷ 1 = 105.
5/21 is already in lowest terms because the GCF of 5 and 21 is 1.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 5 | 1 | 10 |
| 3 and 5 | 1 | 15 |
| 4 and 5 | 1 | 20 |
| 5 and 6 | 1 | 30 |
| 5 and 7 | 1 | 35 |
| 5 and 8 | 1 | 40 |
| 2 and 21 | 1 | 42 |
| 3 and 21 | 3 | 21 |
| 4 and 21 | 1 | 84 |
| 6 and 21 | 3 | 42 |
| 7 and 21 | 7 | 21 |
| 8 and 21 | 1 | 168 |
See also: factors of 5 · factors of 21.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.