The GCF of 12 and 14 is 2. The LCM of 12 and 14 is 84.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 14: 1, 2, 7, 14.
Common factors: 1 and 2. The greatest of these is 2.
12 = 2 × 2 × 3
14 = 2 × 7
GCF: multiply the prime factors both numbers share: 2 = 2.
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 2, so GCF(12, 14) = 2.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, ...
Multiples of 14: 14, 28, 42, 56, 70, 84, 98, ...
The first number in both lists is 84.
2 × 84 = 168 = 12 × 14. This always holds for two numbers, so you can find the LCM as (12 × 14) ÷ 2 = 84.
Divide the top and bottom by the GCF 2: 12/14 = 6/7.
| 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 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 |
See also: factors of 12 · factors of 14 · 12/14 as a decimal.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.