[MAS1]

Originally Posted by burgess

Help required solve math homework problem

What is the least number that should be added to 2497 so that the total is exactly divisible by 5, 6, 4 and 3?

Thanks

I am assuming you mean the least positive number that can be added as there would not be a least negative number.

For a number to be divisible by 3 the sum of the number's digits should be divisible by 3.
For a number to be divisible by 4 the last 2 digits of the number should be divisible by 4.
For a number to be divisible by 5 the last digit of the number should be either 0 or 5.
For a number to be divisible by 6 the number should be even and diviisble by 3.

So to be divisible by 5 we could add 3 to 2497 giving 2500. 2500 is divisible by 5 and 4, but not 3 or 6.

So we keep adding 10. The next number to try would be 13. 2497 + 13 = 2510. 2510 is not divisible by 3.

Let's try adding 23. 23 + 2497 = 2520. 2520 is divisible by 3, 4, 5, and 6.

Our answer is 23.