2. Rampо wrote down several different natural numbers and divided their sum by their product. Then, he erased the smallest of the written numbers and again divided the sum of the remaining numbers by their product. It turned out that the second result was three times larger than the first. Which number did Rampо erase?
Solution. Let $a$ be the deleted number, $S$ be the sum of the remaining numbers, and $P$ be their product. Then

$$
\frac{3(a+S)}{a P}=\frac{S}{P} \text {, i.e., } \frac{1}{3}=\frac{1}{a}+\frac{1}{S} \text { . }
$$

Clearly, $a>3$. Furthermore, since $a<S$ we have

$$
\frac{1}{3}<\frac{1}{a}+\frac{1}{a}=\frac{2}{a}
$$

so $a<6$. Therefore, $a=5$ or $a=4$. For $a=5$, we get $S=7.5$ and this is not a natural number. Finally, for $a=4$, we get $S=12$. Thus, Ramp deleted the number 4.