The least number of five digits which has 123 as a factor is

Options

A. 10037
B. 10086
C. 10081
D. 10063

Answer

To find the least number of five digits that has 123 as a factor, 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 the smallest five-digit number by 123**:
We need to determine how many times 123 can fit into 10,000.
\[ 10,000 \div 123 \approx 81.3008 \]
This means 123 fits into 10,000 about 81 times.

3. **Calculate the product of 123 and 81**:
Now we multiply 123 by 81 to find the largest multiple of 123 that is still a four-digit number.
\[ 123 \times 81 = 9,963 \]

4. **Check the remainder**:
We need to find the remainder when 10,000 is divided by 123 to see how much more we need to reach the next multiple of 123.
\[ 10,000 - 9,963 = 37 \]

5. **Find the next multiple of 123**:
Since 9,963 is less than 10,000, we need to check the next multiple, which is 82.
\[ 123 \times 82 = 10,086 \]

6. **Conclusion**:
The least five-digit number that has 123 as a factor is 10,086.

### Final Answer:
The least number of five digits which has 123 as a factor is **10,086**.