The GCF of 6 and 12 is 6. The LCM of 6 and 12 is 12.
Factors of 6: 1, 2, 3, 6.
Factors of 12: 1, 2, 3, 4, 6, 12.
Common factors: 1, 2, 3 and 6. The greatest of these is 6.
6 = 2 × 3
12 = 2 × 2 × 3
GCF: multiply the prime factors both numbers share: 2 × 3 = 6.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 = 12.
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 6, so GCF(6, 12) = 6.
Multiples of 6: 6, 12, 18, ...
Multiples of 12: 12, 24, ...
The first number in both lists is 12.
6 × 12 = 72 = 6 × 12. This always holds for two numbers, so you can find the LCM as (6 × 12) ÷ 6 = 12.
Divide the top and bottom by the GCF 6: 6/12 = 1/2.
| 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 12 | 2 | 12 |
| 3 and 12 | 3 | 12 |
| 4 and 12 | 4 | 12 |
| 5 and 12 | 1 | 60 |
| 7 and 12 | 1 | 84 |
| 8 and 12 | 4 | 24 |
See also: factors of 6 · factors of 12 · 6/12 as a decimal.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.