The GCF of 21 and 24 is 3. The LCM of 21 and 24 is 168.
Factors of 21: 1, 3, 7, 21.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Common factors: 1 and 3. The greatest of these is 3.
21 = 3 × 7
24 = 2 × 2 × 2 × 3
GCF: multiply the prime factors both numbers share: 3 = 3.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 3 × 7 = 168.
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 3, so GCF(21, 24) = 3.
Multiples of 21: 21, 42, 63, 84, 105, 126, 147, 168, 189, ...
Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, ...
The first number in both lists is 168.
3 × 168 = 504 = 21 × 24. This always holds for two numbers, so you can find the LCM as (21 × 24) ÷ 3 = 168.
Divide the top and bottom by the GCF 3: 21/24 = 7/8.
| 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 24 | 2 | 24 |
| 3 and 24 | 3 | 24 |
| 4 and 24 | 4 | 24 |
| 5 and 24 | 1 | 120 |
| 6 and 24 | 6 | 24 |
| 7 and 24 | 1 | 168 |
See also: factors of 21 · factors of 24.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.