The GCF of 12 and 36 is 12. The LCM of 12 and 36 is 36.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Common factors: 1, 2, 3, 4, 6 and 12. The greatest of these is 12.
12 = 2 × 2 × 3
36 = 2 × 2 × 3 × 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 × 3 × 3 = 36.
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, 36) = 12.
Multiples of 12: 12, 24, 36, 48, ...
Multiples of 36: 36, 72, ...
The first number in both lists is 36.
12 × 36 = 432 = 12 × 36. This always holds for two numbers, so you can find the LCM as (12 × 36) ÷ 12 = 36.
Divide the top and bottom by the GCF 12: 12/36 = 1/3.
| 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 36 | 2 | 36 |
| 3 and 36 | 3 | 36 |
| 4 and 36 | 4 | 36 |
| 5 and 36 | 1 | 180 |
| 6 and 36 | 6 | 36 |
| 7 and 36 | 1 | 252 |
See also: factors of 12 · factors of 36.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.