Find the least number of 5 digits which is exactly divisible by 456?

Step-by-Step Solution

To find the smallest 5-digit number divisible by 456, follow this systematic approach:

1. Identify the smallest 5-digit number:

   • The smallest 5-digit number is 10,000.

2. Divide by the target divisor:

   • Divide 10,000 by 456 to see how close it is to the next multiple.

   • 10,000 ÷ 456 = 21 with a remainder of 424.

   • This means 10,000 is 424 units past a multiple of 456.

3. Determine the adjustment:

   • To reach the next multiple of 456, calculate how much more needs to be added to the remainder:

   • 456 - 424 = 32.

4. Find the required number:

   • Add this difference to the smallest 5-digit number:

   • 10,000 + 32 = 10,032.