5,6,7 |
| :---: | :---: | :---: |
|  | [ Divisibility of numbers. General properties ] |  |
|  | [ Decimal number system ] |  |
|  | Case analysis |  |

Which digits can stand in place of the letters in the example $A B \cdot C=D E$, if different letters represent different digits and the digits are written from left to right in ascending order?
Let's consider the largest possible values of the number $DE$. The numbers 89 and 79 are prime, so they do not fit. Next, let's consider the number 78, and check its single-digit divisors to get the answer. Further checking can confirm that this answer is unique.

## Answer

$13 \cdot 6=78$.