The GCF of 6 and 14 is 2. The LCM of 6 and 14 is 42.
Factors of 6: 1, 2, 3, 6.
Factors of 14: 1, 2, 7, 14.
Common factors: 1 and 2. The greatest of these is 2.
6 = 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 × 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 2, so GCF(6, 14) = 2.
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
Multiples of 14: 14, 28, 42, 56, ...
The first number in both lists is 42.
2 × 42 = 84 = 6 × 14. This always holds for two numbers, so you can find the LCM as (6 × 14) ÷ 2 = 42.
Divide the top and bottom by the GCF 2: 6/14 = 3/7.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 6 | 2 | 6 |
| 3 and 6 | 3 | 6 |
| 4 and 6 | 2 | 12 |
| 5 and 6 | 1 | 30 |
| 6 and 7 | 1 | 42 |
| 6 and 8 | 2 | 24 |
| 2 and 14 | 2 | 14 |
| 3 and 14 | 1 | 42 |
| 4 and 14 | 2 | 28 |
| 5 and 14 | 1 | 70 |
| 7 and 14 | 7 | 14 |
| 8 and 14 | 2 | 56 |
See also: factors of 6 · factors of 14 · 6/14 as a decimal.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.