Max value of x/phi(x)

[Alonso Del Arte]

Does anyone know what the maximum possible value of x/phi(x) can be
(where phi is Euler's totient function)? Is there a theorem in regards
to this?

 From some playing around with Mathematica it seems to me that the
value can be made as large as one wants by choosing a sufficiently
large highly composite number, but I'm wondering if x/phi(x) is
bounded by some property of x, such as its square root.

Alonso Delarte