On the centroid of a Leavitt path algebra

We describe the centroid of some Leavitt path algebras. More precisely, we show that for Leavitt path algebras over a field $K$ that are simple its centroid is isomorphic to $K$, and for prime Leavitt path algebras its centroid is isomorphic to $K$ except if the graph is a row-finite comet, in which case the centroid is isomorphic to $K[x,x^{-1}]$.