The GCF of 12 and 21 is 3. The LCM of 12 and 21 is 84.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 21: 1, 3, 7, 21.
Common factors: 1 and 3. The greatest of these is 3.
12 = 2 × 2 × 3
21 = 3 × 7
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 × 3 × 7 = 84.
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(12, 21) = 3.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, ...
Multiples of 21: 21, 42, 63, 84, 105, ...
The first number in both lists is 84.
3 × 84 = 252 = 12 × 21. This always holds for two numbers, so you can find the LCM as (12 × 21) ÷ 3 = 84.
Divide the top and bottom by the GCF 3: 12/21 = 4/7.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 12 | 2 | 12 |
| 3 and 12 | 3 | 12 |
| 4 and 12 | 4 | 12 |
| 5 and 12 | 1 | 60 |
| 6 and 12 | 6 | 12 |
| 7 and 12 | 1 | 84 |
| 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 12 · factors of 21.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.