Problem 9.2. The least common multiple of four pairwise distinct numbers is 165. What is the maximum value that the sum of these numbers can take?
Answer: 268.

Solution. Since 165 is the least common multiple of four numbers, these numbers are divisors of 165. To maximize the sum of these numbers, it is sufficient to take the four largest divisors of 165. If one of them is the number 165 itself, then the LCM will definitely be equal to it.

Then the maximum sum will be

$$
165+\frac{165}{3}+\frac{165}{5}+\frac{165}{11}=165+55+33+15=268
$$