If 7x8 is exactly divisible by 3, then the least value of x is

Options

A. 3
B. 0
C. 6
D. 9

Answer

To solve the problem, we need to find the least value of \( x \) such that the number \( 7x8 \) is exactly divisible by 3.

### Step-by-Step Solution:

1. **Understanding the Problem**: We need to determine the value of \( x \) in the number \( 7x8 \) so that it is divisible by 3. A number is divisible by 3 if the sum of its digits is divisible by 3.

2. **Identifying the Digits**: The digits of the number \( 7x8 \) are 7, \( x \), and 8.

3. **Calculating the Sum of the Digits**: We can express the sum of the digits as:
\[ 7 + x + 8 = 15 + x \]

4. **Finding the Condition for Divisibility by 3**: We need \( 15 + x \) to be divisible by 3. Since 15 is already divisible by 3 (as \( 15 \div 3 = 5 \)), we need \( x \) itself to be divisible by 3.

5. **Determining Possible Values for \( x \)**: The possible values of \( x \) (which is a single digit) that are divisible by 3 are:
- \( 0 \)
- \( 3 \)
- \( 6 \)
- \( 9 \)

6. **Finding the Least Value of \( x \)**: Among the possible values \( 0, 3, 6, 9 \), the least value is:
\[ x = 0 \]

### Conclusion:
Thus, the least value of \( x \) for which \( 7x8 \) is exactly divisible by 3 is \( \boxed{0} \).