Question 74
Show that for any positive integers $a, b$, and $c$,
$$
a b c \operatorname{lcm}(a, b, c) \geq \operatorname{lcm}(b, c) \operatorname{lcm}(c, a) \operatorname{lcm}(a, b),
$$
where lcm denotes the least common multiple.
$$
a b c \operatorname{lcm}(a, b, c) \geq \operatorname{lcm}(b, c) \operatorname{lcm}(c, a) \operatorname{lcm}(a, b),
$$
where lcm denotes the least common multiple.