What is the least number multiplied to 100, so that the number becomes a multiple of 15?

Options

A. 5
B. 2
C. 4
D. 3

Answer

To solve the problem of finding the least number that must be multiplied by 100 in order for the product to be a multiple of 15, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find the smallest integer \( n \) such that \( 100 \times n \) is a multiple of 15.

2. **Identify the Multiples of 15**: A number is a multiple of 15 if it can be expressed as \( 15k \) for some integer \( k \).

3. **Check the Prime Factorization**:
- The prime factorization of 15 is \( 3 \times 5 \).
- The prime factorization of 100 is \( 2^2 \times 5^2 \).

4. **Determine the Required Factors**:
- For \( 100n \) to be a multiple of 15, it must include at least one factor of 3 and one factor of 5.
- Since \( 100 \) already has \( 5^2 \), we only need to introduce a factor of 3.

5. **Calculate the Least Number**:
- The least number \( n \) that we need to multiply by 100 to introduce a factor of 3 is \( 3 \) itself.
- Therefore, we multiply \( 100 \) by \( 3 \):
\[ 100 \times 3 = 300 \]

6. **Verify the Result**:
- Now, check if \( 300 \) is a multiple of 15:
\[ 300 \div 15 = 20 \]
- Since \( 20 \) is an integer, \( 300 \) is indeed a multiple of 15.

7. **Conclusion**: The least number that must be multiplied to 100 so that the product becomes a multiple of 15 is \( 3 \).

### Final Answer:
The least number is \( 3 \).