LCM equals Factorial

Find the sum of all natural numbers \(n\) such that

\[ \text{lcm}(1,2,3,\ldots, n) = n!\]

Notations:

  • \(\text{lcm}(\cdot) \) denotes the lowest common multiple function.
  • \(!\) is the factorial notation. For example, \(8! = 1\times2\times3\times\cdots\times8 \).
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