To find the least number of five digits that is exactly divisible by 654, we need to follow a structured approach:
1. Identify the smallest five-digit number:
The smallest number that has five digits is 10000.
2. Find the first five-digit number divisible by 654:
To do this, we need to determine the remainder when 10000 is divided by 654.
3. Calculate the remainder:
When 10000 is divided by 654, it leaves a remainder. Let's denote this remainder as "r".
4. Find the needed increment:
To reach the next number that is exactly divisible by 654, we need to add (654 - r) to 10000.
5. Conclusion:
After performing these calculations, the least number of five digits which is exactly divisible by 654 is found to be 10464.
Thus, the correct answer is:
a. 10464
