phi(n) Euler's Totient Function:

Given the group (Z/nZ)* would I be correct in saying that L = lcm(d1,...dk) where d1,...,dk are the distinct orders of the elements of (Z/nZ)* is the smallest integer for which a^L=1 for all elements of (Z/nZ)*?

Secondly, since di | |(Z/nZ)*| = phi(n) for i=1,...,k am I correct in saying that L is less than or equal to phi(n)?

Main question(s):

When is phi(n)/L an integer (always?)? More generally, can we write phi(n)/L as f(phi(n)) some function of phi(n)? When is phi(n) an element of (Z/nZ)*?

Cheers. Any help (on any of the questions) much appreciated.