The GCF of 14 and 21 is 7. The LCM of 14 and 21 is 42.
Factors of 14: 1, 2, 7, 14.
Factors of 21: 1, 3, 7, 21.
Common factors: 1 and 7. The greatest of these is 7.
14 = 2 × 7
21 = 3 × 7
GCF: multiply the prime factors both numbers share: 7 = 7.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 3 × 7 = 42.
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 7, so GCF(14, 21) = 7.
Multiples of 14: 14, 28, 42, 56, ...
Multiples of 21: 21, 42, 63, ...
The first number in both lists is 42.
7 × 42 = 294 = 14 × 21. This always holds for two numbers, so you can find the LCM as (14 × 21) ÷ 7 = 42.
Divide the top and bottom by the GCF 7: 14/21 = 2/3.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 14 | 2 | 14 |
| 3 and 14 | 1 | 42 |
| 4 and 14 | 2 | 28 |
| 5 and 14 | 1 | 70 |
| 6 and 14 | 2 | 42 |
| 7 and 14 | 7 | 14 |
| 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 14 · factors of 21.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.