The GCF of 27 and 36 is 9. The LCM of 27 and 36 is 108.
Factors of 27: 1, 3, 9, 27.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Common factors: 1, 3 and 9. The greatest of these is 9.
27 = 3 × 3 × 3
36 = 2 × 2 × 3 × 3
GCF: multiply the prime factors both numbers share: 3 × 3 = 9.
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 9, so GCF(27, 36) = 9.
Multiples of 27: 27, 54, 81, 108, 135, ...
Multiples of 36: 36, 72, 108, 144, ...
The first number in both lists is 108.
9 × 108 = 972 = 27 × 36. This always holds for two numbers, so you can find the LCM as (27 × 36) ÷ 9 = 108.
Divide the top and bottom by the GCF 9: 27/36 = 3/4.
| Numbers | GCF | LCM |
|---|---|---|
| 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 |
| 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 27 · factors of 36.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.