  Assume that $f:(\mathbb{C}^n,0) \to (\mathbb{C},0)$ is an analytic function
germ at the origin with only isolated singularity. Let $\mu$ and $\tau$ be the
corresponding Milnor and Tjurina numbers. We show that $\dfrac{\mu}{\tau} \leq
n$. As an application, we give a lower bound for the Tjurina number in terms of
$n$ and the multiplicity of $f$ at the origin.
