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What integers can be represented as $\textrm{lcm}(a, b) + \textrm{lcm}(b, c) + \textrm{lcm}(c, a)$?

Find all integers $n$ that can be written as $n = \textrm{lcm}(a, b) + \textrm{lcm}(b, c) + \textrm{lcm}(c, a)$ where $a$, $b$, $c$ are all integers.

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