The GCF of 27 and 45 is 9. The LCM of 27 and 45 is 135.
Factors of 27: 1, 3, 9, 27.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1, 3 and 9. The greatest of these is 9.
27 = 3 × 3 × 3
45 = 3 × 3 × 5
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: 3 × 3 × 3 × 5 = 135.
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, 45) = 9.
Multiples of 27: 27, 54, 81, 108, 135, 162, ...
Multiples of 45: 45, 90, 135, 180, ...
The first number in both lists is 135.
9 × 135 = 1,215 = 27 × 45. This always holds for two numbers, so you can find the LCM as (27 × 45) ÷ 9 = 135.
Divide the top and bottom by the GCF 9: 27/45 = 3/5.
| 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 45 | 1 | 90 |
| 3 and 45 | 3 | 45 |
| 4 and 45 | 1 | 180 |
| 5 and 45 | 5 | 45 |
| 6 and 45 | 3 | 90 |
| 7 and 45 | 1 | 315 |
See also: factors of 27 · factors of 45.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.