2. Klárka made a mistake when multiplying two two-digit numbers, and thus her result was 400 less than the correct result. To check, she divided the number she got by the smaller of the multiplied numbers. This time she calculated correctly and got an incomplete quotient of 67 and a remainder of 56. Which numbers did Klárka multiply?
2. Let $x$ be the smaller and $y$ the larger of the multiplied numbers. According to the problem, we have $xy - 400 = 67x + 56$, or equivalently,

$$
x(y-67) = 456 \text{.}
$$

The number $x$ is thus a two-digit divisor of the number $456 = 2^3 \cdot 3 \cdot 19$. From the problem, it also follows that the number $x$ is greater than the corresponding remainder 56. The smallest such $x$ is $x = 3 \cdot 19 = 57$. For any other such divisor, $x \geq 4 \cdot 19 = 76$ and $y - 67 \leq 2 \cdot 3 = 6$, so $y \leq 73 < x$, which contradicts the chosen notation $x < y$. Therefore, $x = 57$ and $y = 75$. It is easy to verify that these numbers satisfy the conditions of the problem.

Conclusion. Klárka multiplied the numbers 57 and 75.

For a complete solution, award 6 points. This includes solutions that verify all 16 divisors of the number 456 in (1). Award 3 points for finding equation (1) or an equivalent relationship, 2 points for analyzing its solutions, and 1 point for the check, i.e., verifying that the pair $(x, y) = (57, 75)$ satisfies all conditions of the problem. For simply guessing the numbers (without setting up the equation) and performing the check, award a total of 2 points.