The least number of five digits exactly divistble by 88 is :

Options

A. a) 10032
B. b) 10132
C. c) 10088
D. d) 10023

Answer

To find the least number of five digits that is exactly divisible by 88, we can follow these steps:

### Step-by-step Solution:

1. **Identify the smallest five-digit number**:
The smallest five-digit number is 10,000.

2. **Divide 10,000 by 88**:
We need to check if 10,000 is divisible by 88.
\[ 10,000 \div 88 \approx 113.6363 \]
This means 10,000 is not exactly divisible by 88.

3. **Calculate the remainder**:
To find the remainder, we can multiply the integer part of the division by 88 and subtract it from 10,000.
\[ 88 \times 113 = 9,964 \]
Now, subtract this from 10,000:
\[ 10,000 - 9,964 = 36 \]
So, the remainder when 10,000 is divided by 88 is 36.

4. **Find the next multiple of 88**:
Since there is a remainder of 36, we need to add the difference to reach the next multiple of 88.
\[ 88 - 36 = 52 \]
Therefore, we need to add 52 to 10,000 to find the next multiple of 88.

5. **Calculate the least five-digit number divisible by 88**:
Now, add 52 to 10,000:
\[ 10,000 + 52 = 10,052 \]

6. **Verify divisibility**:
Finally, we can verify that 10,052 is divisible by 88:
\[ 10,052 \div 88 = 114 \]
This confirms that 10,052 is exactly divisible by 88.

### Conclusion:
The least number of five digits exactly divisible by 88 is **10,056**.