The smallest number divisible by both 5 and 9 is 45.
Understanding the Least Common Multiple (LCM)
To find the smallest number divisible by two or more numbers, we're looking for the Least Common Multiple (LCM). The LCM is the smallest positive integer that is a multiple of all the given numbers.
Finding the LCM of 5 and 9
Here's how we determine the LCM of 5 and 9, as explained in the reference:
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50...
- Multiples of 9: 9, 18, 27, 36, 45, 54...
As you can see, the smallest number that appears in both lists is 45.
Table of Multiples
To visualize, here's a table showing the multiples of both 5 and 9:
| Multiples of 5 | Multiples of 9 |
|---|---|
| 5 | 9 |
| 10 | 18 |
| 15 | 27 |
| 20 | 36 |
| 25 | 45 |
| 30 | |
| 35 | |
| 40 | |
| 45 |
Conclusion
Therefore, the smallest number divisible by both 5 and 9 is 45. This is their LCM.
