The GCF of 12 and 48 is 12. The LCM of 12 and 48 is 48.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.
Common factors: 1, 2, 3, 4, 6 and 12. The greatest of these is 12.
12 = 2 × 2 × 3
48 = 2 × 2 × 2 × 2 × 3
GCF: multiply the prime factors both numbers share: 2 × 2 × 3 = 12.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 2 × 2 × 3 = 48.
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 12, so GCF(12, 48) = 12.
Multiples of 12: 12, 24, 36, 48, 60, ...
Multiples of 48: 48, 96, ...
The first number in both lists is 48.
12 × 48 = 576 = 12 × 48. This always holds for two numbers, so you can find the LCM as (12 × 48) ÷ 12 = 48.
Divide the top and bottom by the GCF 12: 12/48 = 1/4.
| 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 48 | 2 | 48 |
| 3 and 48 | 3 | 48 |
| 4 and 48 | 4 | 48 |
| 5 and 48 | 1 | 240 |
| 6 and 48 | 6 | 48 |
| 7 and 48 | 1 | 336 |
See also: factors of 12 · factors of 48.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.