Simple but sweet

Let \(n\), \(a\), \(b\) and \(c\) be positive integers such that \(\frac {1}{2} n = a^2\), \(\frac{1}{3} n = b^3\) and \(\frac{1}{5} n = c^5\).

Find the smallest possible number of positive divisors of \(n\) (inclusive of 1 and itself).

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