  We give an expression for the {\L}ojasiewicz exponent of a set of ideals
which are pieces of a weighted homogeneous filtration. We also study the
application of this formula to the computation of the {\L}ojasiewicz exponent
of the gradient of a semi-weighted homogeneous function $(\C^n,0)\to (\C,0)$
with an isolated singularity at the origin.
