The GCF of 20 and 45 is 5. The LCM of 20 and 45 is 180.
Factors of 20: 1, 2, 4, 5, 10, 20.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1 and 5. The greatest of these is 5.
20 = 2 × 2 × 5
45 = 3 × 3 × 5
GCF: multiply the prime factors both numbers share: 5 = 5.
LCM: multiply every prime the maximum number of times it appears in either number: 2 × 2 × 3 × 3 × 5 = 180.
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 5, so GCF(20, 45) = 5.
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, ...
Multiples of 45: 45, 90, 135, 180, 225, ...
The first number in both lists is 180.
5 × 180 = 900 = 20 × 45. This always holds for two numbers, so you can find the LCM as (20 × 45) ÷ 5 = 180.
Divide the top and bottom by the GCF 5: 20/45 = 4/9.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 20 | 2 | 20 |
| 3 and 20 | 1 | 60 |
| 4 and 20 | 4 | 20 |
| 5 and 20 | 5 | 20 |
| 6 and 20 | 2 | 60 |
| 7 and 20 | 1 | 140 |
| 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 20 · factors of 45.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.