There are three common multiples of 5 and 25 that are less than 100.
Understanding Common Multiples
First, let's understand what a common multiple is. A common multiple of two or more numbers is a number that is a multiple of each of those numbers.
- Multiples of 5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100,...
- Multiples of 25: 25, 50, 75, 100, 125,...
Notice that all multiples of 25 are also multiples of 5. Therefore, to find the common multiples of 5 and 25, we only need to consider the multiples of 25.
Identifying Common Multiples Less Than 100
We are looking for common multiples that are less than 100. From the list of multiples of 25, we can easily identify them:
- 25
- 50
- 75
These are the only multiples of 25 that are less than 100, and they are also common multiples of 5 and 25.
Summary
The common multiples of 5 and 25 less than 100 are 25, 50, and 75. According to the reference, these are indeed the correct common multiples under 100, as stated: 25 50 75 100. Since we are looking for the number of common multiples that are less than 100, we exclude 100, giving us a total of three multiples.
| Common Multiple | Less Than 100 |
|---|---|
| 25 | Yes |
| 50 | Yes |
| 75 | Yes |
| 100 | No |
Therefore, the number of common multiples of 5 and 25 that are less than 100 is 3.
