When you know $e,d,N$, you can calculate $ed-1$, which is a multiple of $\Phi(n)$. I guess that's what you meant by

> $\Phi(n)$ will have multiple values.

The sentence itself is wrong, though. As a function it does not have "multiple values" for a fixed $n$. You know *a multiple of the value*.

There are various algorithms to do this:

- A probabilistic algorithm was given in the original RSA paper [A method for obtaining digital signatures and public-key cryptosystems](http://dl.acm.org/citation.cfm?id=359342) by Rivest, Shamir and Adleman, 1978
- A deterministic algorithm was given in [Computing the RSA Secret Key is Deterministic Polynomial Time Equivalent to Factoring](https://www.iacr.org/archive/crypto2004/31520213/det.pdf) by May, 2004.
- [This answer on SO](https://stackoverflow.com/a/5747441) references a different paper called *Twenty Years of Attacks on the RSA Cryptosystem* by Boneh, 1999.

This looks like a homework question, so I won't give an explicit algorithm.