The GCF of 10 and 45 is 5. The LCM of 10 and 45 is 90.
Factors of 10: 1, 2, 5, 10.
Factors of 45: 1, 3, 5, 9, 15, 45.
Common factors: 1 and 5. The greatest of these is 5.
10 = 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 × 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 5, so GCF(10, 45) = 5.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, ...
Multiples of 45: 45, 90, 135, ...
The first number in both lists is 90.
5 × 90 = 450 = 10 × 45. This always holds for two numbers, so you can find the LCM as (10 × 45) ÷ 5 = 90.
Divide the top and bottom by the GCF 5: 10/45 = 2/9.
| Numbers | GCF | LCM |
|---|---|---|
| 2 and 10 | 2 | 10 |
| 3 and 10 | 1 | 30 |
| 4 and 10 | 2 | 20 |
| 5 and 10 | 5 | 10 |
| 6 and 10 | 2 | 30 |
| 7 and 10 | 1 | 70 |
| 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 10 · factors of 45.
Different numbers? Use the GCF and LCM calculator (any amount of numbers) or browse all GCF and LCM pairs.