Which smallest number will have 15,20,25,31 nd 43 as reminder respectively when divided by 20, 25, 30, 36,48
explain the answer you found

I assume by smallest number, you're really looking for the smallest *positive* number.

Notice that -5 fits all these requirements:







Any number of the form will also satisfy these conditions, where and is the least common multiple of the moduli. You have



so the least positive number would be achieved with , giving 3595 as the answer. (Verified with a script.)