The GCF of 30 and 45 is 15. The LCM of 30 and 45 is 90.
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1, 3, 5 and 15. The greatest of these is 15.
30 = 2 × 3 × 5
45 = 3 × 3 × 5
GCF: multiply the prime factors both numbers share: 3 × 5 = 15.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 3 × 3 × 5 = 90.
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 15, so GCF(30, 45) = 15.
Multiples of 30: 30, 60, 90, 120, ...
Multiples of 45: 45, 90, 135, ...
The first number in both lists is 90.
15 × 90 = 1,350 = 30 × 45. This always holds for two numbers, so you can find the LCM as (30 × 45) ÷ 15 = 90.
Divide the top and bottom by the GCF 15: 30/45 = 2/3.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 30 | 2 | 30 |
| 3 and 30 | 3 | 30 |
| 4 and 30 | 2 | 60 |
| 5 and 30 | 5 | 30 |
| 6 and 30 | 6 | 30 |
| 7 and 30 | 1 | 210 |
| 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 30 · factors of 45.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.