The GCF of 21 and 23 is 1. The LCM of 21 and 23 is 483.
21 and 23 share no common factor except 1, so they are coprime (relatively prime). When two numbers are coprime their LCM is simply their product: 21 × 23 = 483.
Factors of 21: 1, 3, 7, 21.
Factors of 23: 1, 23.
Common factors: 1. The greatest of these is 1.
21 = 3 × 7
23 = 23 (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: 3 × 7 × 23 = 483.
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(21, 23) = 1.
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, ...
Multiples of 23: 23, 46, 69, 92, 115, 138, 161, 184, 207, ...
The first number in both lists is 483.
1 × 483 = 483 = 21 × 23. This always holds for two numbers, so you can find the LCM as (21 × 23) ÷ 1 = 483.
21/23 is already in lowest terms because the GCF of 21 and 23 is 1.
| Numbers | GCF | LCM |
|---|---|---|
| 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 |
| 2 and 23 | 1 | 46 |
| 3 and 23 | 1 | 69 |
| 4 and 23 | 1 | 92 |
| 5 and 23 | 1 | 115 |
| 6 and 23 | 1 | 138 |
| 7 and 23 | 1 | 161 |
See also: factors of 21 · factors of 23.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.