The GCF of 24 and 45 is 3. The LCM of 24 and 45 is 360.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1 and 3. The greatest of these is 3.
24 = 2 × 2 × 2 × 3
45 = 3 × 3 × 5
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 × 2 × 3 × 3 × 5 = 360.
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(24, 45) = 3.
Multiples of 24: 24, 48, 72, 96, 120, 144, 168, 192, 216, ...
Multiples of 45: 45, 90, 135, 180, 225, 270, 315, 360, 405, ...
The first number in both lists is 360.
3 × 360 = 1,080 = 24 × 45. This always holds for two numbers, so you can find the LCM as (24 × 45) ÷ 3 = 360.
Divide the top and bottom by the GCF 3: 24/45 = 8/15.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 24 | 2 | 24 |
| 3 and 24 | 3 | 24 |
| 4 and 24 | 4 | 24 |
| 5 and 24 | 1 | 120 |
| 6 and 24 | 6 | 24 |
| 7 and 24 | 1 | 168 |
| 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 24 · factors of 45.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.