if a number is divided by 72 it leaves 71 as remainder. The same number divided by 81 leaves 80 as remainder
QUOTIENT
DIVISOR)DIVIDEND
REMAINDER
In a division, if the remainder is 1 less than the divisor,
then the dividend must have been 1 less than a multiple of
the divisor, like this:
3
7)27
21
6
Here the remainder is 6, 1 less than the divisor 7, because
the 27 is 1 less than 28, a multiple of 7
That's true in both these cases. So 1 less than any common
multiple of 72 and 80 must be a solution.
The least common multiple of 72 and 81 is 648, so the smallest
answer is 648-1 or 647.
However there are infinitely many answers. The next common
multiple of 72 and 80 is 1296, so 1295 is also a solution, etc., etc.
Edwin