How do I show that a likelihood ratio test depends on data only through the value of a sufficient statistic?

I am not sure how to show this, even though it seems obvious. Since L(\omega_{0}) is the maximum of the likelihood function for all values of \theta in \omega_{0} isn't is clear that that the ratio of \frac{L(\omega_{0})}{L(\omega)} is based on sufficient statistics because the part of the likelihood functions not associated withe the data would be the same and cancle out?