The GCF of 12 and 30 is 6. The LCM of 12 and 30 is 60.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Common factors: 1, 2, 3 and 6. The greatest of these is 6.
12 = 2 × 2 × 3
30 = 2 × 3 × 5
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 × 5 = 60.
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(12, 30) = 6.
Multiples of 12: 12, 24, 36, 48, 60, 72, ...
Multiples of 30: 30, 60, 90, ...
The first number in both lists is 60.
6 × 60 = 360 = 12 × 30. This always holds for two numbers, so you can find the LCM as (12 × 30) ÷ 6 = 60.
Divide the top and bottom by the GCF 6: 12/30 = 2/5.
| 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 30 | 2 | 30 |
| 3 and 30 | 3 | 30 |
| 4 and 30 | 2 | 60 |
| 5 and 30 | 5 | 30 |
| 6 and 30 | 6 | 30 |
| 7 and 30 | 1 | 210 |
See also: factors of 12 · factors of 30.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.