The GCF of 12 and 27 is 3. The LCM of 12 and 27 is 108.
Factors of 12: 1, 2, 3, 4, 6, 12.
Factors of 27: 1, 3, 9, 27.
Common factors: 1 and 3. The greatest of these is 3.
12 = 2 × 2 × 3
27 = 3 × 3 × 3
GCF: multiply the prime factors both numbers share: 3 = 3.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 3 × 3 = 108.
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 3, so GCF(12, 27) = 3.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, ...
Multiples of 27: 27, 54, 81, 108, 135, ...
The first number in both lists is 108.
3 × 108 = 324 = 12 × 27. This always holds for two numbers, so you can find the LCM as (12 × 27) ÷ 3 = 108.
Divide the top and bottom by the GCF 3: 12/27 = 4/9.
| 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 27 | 1 | 54 |
| 3 and 27 | 3 | 27 |
| 4 and 27 | 1 | 108 |
| 5 and 27 | 1 | 135 |
| 6 and 27 | 3 | 54 |
| 7 and 27 | 1 | 189 |
See also: factors of 12 · factors of 27.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.