Question 5
Find all natural numbers $n$ for which there is no triple of natural numbers $(a, b, c)$ such that the following equation holds:
$$
n=\frac{a \cdot \operatorname{lcm}(b, c)+b \cdot \operatorname{lcm}(c, a)+c \cdot \operatorname{lcm}(a, b)}{\operatorname{lcm}(a, b, c)}
$$
$$
n=\frac{a \cdot \operatorname{lcm}(b, c)+b \cdot \operatorname{lcm}(c, a)+c \cdot \operatorname{lcm}(a, b)}{\operatorname{lcm}(a, b, c)}
$$