  For an ideal of smooth functions that is either {\L}ojasiewicz or weakly
{\L}ojasiewicz, we give a complete characterization of the ideal of functions
vanishing on its variety in terms of the global {\L}ojasiewicz radical and
Whitney closure. We also prove that the {\L}ojasiewicz radical of such an ideal
is analytic-like in the sense that its saturation equals its Whitney closure.
This allows us to recover in a different way Nullstellensatz results due to
Bochnak and Adkins-Leahy and answer positively a modification of the
Nullstellensatz conjecture due to Bochnak.
