What is the least number that must be ADDED to 2497 to make it exactly divisible by 23?

First divide: $23\times 108=2484$, so 2497 leaves remainder 13. To reach the NEXT multiple we top up by 23 − 13 = 10, giving $2507=23\times 109$. The trap is 13: that is the amount you would SUBTRACT to fall back to 2484. Adding the divisor 23 itself also works arithmetically but is not the least such number.