When dividing a certain number $m$ by 13 and 15, the same quotient was obtained, but the first division had a remainder of 8, while the second division had no remainder.

Find the number $m$.
How to determine how much the remainder of division by 13 is greater than the remainder of division by 15, if the quotient is known

## Solution

The number 13 is 2 less than 15. Therefore, with the same quotient \( n \), the remainder of division by 13 is \( 2n \) greater than the remainder of division by 15, i.e., \( 2n = 8 \). From this, the dividend is \( 15 \cdot 4 = 13 \cdot 4 + 8 = 60 \).

## Answer

60.