The GCF of 8 and 12 is 4. The LCM of 8 and 12 is 24.
Factors of 8: 1, 2, 4, 8.
Factors of 12: 1, 2, 3, 4, 6, 12.
Common factors: 1, 2 and 4. The greatest of these is 4.
8 = 2 × 2 × 2
12 = 2 × 2 × 3
GCF: multiply the prime factors both numbers share: 2 × 2 = 4.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 3 = 24.
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 4, so GCF(8, 12) = 4.
Multiples of 8: 8, 16, 24, 32, ...
Multiples of 12: 12, 24, 36, ...
The first number in both lists is 24.
4 × 24 = 96 = 8 × 12. This always holds for two numbers, so you can find the LCM as (8 × 12) ÷ 4 = 24.
Divide the top and bottom by the GCF 4: 8/12 = 2/3.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 8 | 2 | 8 |
| 3 and 8 | 1 | 24 |
| 4 and 8 | 4 | 8 |
| 5 and 8 | 1 | 40 |
| 6 and 8 | 2 | 24 |
| 7 and 8 | 1 | 56 |
| 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 |
See also: factors of 8 · factors of 12 · 8/12 as a decimal.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.