If a number is divisible by two numbers x and y, then it is divisible/not divisible by their product `x xx y`

Answer

To solve the question, we need to determine if a number that is divisible by two numbers \( x \) and \( y \) is also divisible by their product \( x \times y \).

### Step-by-Step Solution:

1. **Assume a Number**: Let's assume a number, say \( 48 \).

2. **Choose Values for \( x \) and \( y \)**: Let's take \( x = 4 \) and \( y = 8 \).

3. **Check Divisibility by \( x \)**:
- Calculate \( 48 \div 4 \).
- \( 48 \div 4 = 12 \) (which is an integer).
- Therefore, \( 48 \) is divisible by \( 4 \).

4. **Check Divisibility by \( y \)**:
- Calculate \( 48 \div 8 \).
- \( 48 \div 8 = 6 \) (which is also an integer).
- Therefore, \( 48 \) is divisible by \( 8 \).

5. **Calculate the Product \( x \times y \)**:
- Calculate \( 4 \times 8 \).
- \( 4 \times 8 = 32 \).

6. **Check Divisibility by \( x \times y \)**:
- Now, check if \( 48 \) is divisible by \( 32 \).
- Calculate \( 48 \div 32 \).
- \( 48 \div 32 = 1.5 \) (which is not an integer).
- Therefore, \( 48 \) is **not** divisible by \( 32 \).

7. **Conclusion**: Since \( 48 \) is divisible by both \( 4 \) and \( 8 \), but not by their product \( 32 \), we conclude that a number can be divisible by two numbers \( x \) and \( y \) but not necessarily by their product \( x \times y \).

### Final Answer:
A number that is divisible by two numbers \( x \) and \( y \) is **not necessarily divisible** by their product \( x \times y \).

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