We prove that a classical theorem of McAdam [Proc. Amer. Math. Soc. 80 (1980), pp. 555–559] about the analytic spread of an ideal in a Noetherian local ring is true for divisorial filtrations on an excellent local domain R R which is either of equicharacteristic zero or of dimension ≤ 3 \le 3 . In fact, the proof is valid whenever resolution of singularities holds.