# Sixfold fun in 2015, Part 37

$S=\sum_{d|12090}\frac{1}{\phi(d)}$

Find the smallest positive integer $$a$$ such that $$a\times S$$ is an integer.

Clarifications

• The sum $$S$$ is taken over all 32 positive integer divisors $$d$$ of $$12090=6\times 2015$$

• $$\phi(d)$$ denotes the Euler's totient function.

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