The GCF of 9 and 45 is 9. The LCM of 9 and 45 is 45.
Factors of 9: 1, 3, 9.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1, 3 and 9. The greatest of these is 9.
9 = 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 × 5 = 45.
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(9, 45) = 9.
Multiples of 9: 9, 18, 27, 36, 45, 54, ...
Multiples of 45: 45, 90, ...
The first number in both lists is 45.
9 × 45 = 405 = 9 × 45. This always holds for two numbers, so you can find the LCM as (9 × 45) ÷ 9 = 45.
Divide the top and bottom by the GCF 9: 9/45 = 1/5.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 9 | 1 | 18 |
| 3 and 9 | 3 | 9 |
| 4 and 9 | 1 | 36 |
| 5 and 9 | 1 | 45 |
| 6 and 9 | 3 | 18 |
| 7 and 9 | 1 | 63 |
| 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 9 · factors of 45.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.