The GCF of 36 and 45 is 9. The LCM of 36 and 45 is 180.
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1, 3 and 9. The greatest of these is 9.
36 = 2 × 2 × 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: 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 9, so GCF(36, 45) = 9.
Multiples of 36: 36, 72, 108, 144, 180, 216, ...
Multiples of 45: 45, 90, 135, 180, 225, ...
The first number in both lists is 180.
9 × 180 = 1,620 = 36 × 45. This always holds for two numbers, so you can find the LCM as (36 × 45) ÷ 9 = 180.
Divide the top and bottom by the GCF 9: 36/45 = 4/5.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 36 | 2 | 36 |
| 3 and 36 | 3 | 36 |
| 4 and 36 | 4 | 36 |
| 5 and 36 | 1 | 180 |
| 6 and 36 | 6 | 36 |
| 7 and 36 | 1 | 252 |
| 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 36 · factors of 45.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.