Question 810486
if a number is divided by 72 it leaves 71 as remainder. The same number divided by 81 leaves 80 as remainder
<pre>

       <u> QUOTIENT</u>
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:
        
     <u>  3</u>
    7)27
      <u>21</u>
       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</pre>