  L\^e numbers were introduced by Massey with the purpose of numerically
controlling the topological properties of families of non-isolated hypersurface
singularities and describing the topology associated with a function with
non-isolated singularities. They are a generalization of the Milnor number for
isolated hypersurface singularities.
  In this note the authors investigate the composite of an arbitrary
square-free f and $z^2$. They get a formula for the L\^e numbers of the
composite, and consider two applications of these numbers. The first
application is concerned with the extent to which the L\^e numbers are
invariant in a family of functions which satisfy some equisingularity
condition, the second is a quick proof of a new formula for the Euler
obstruction of a hypersurface singularity. Several examples are computed using
this formula including any X defined by a function which only has transverse
D(q,p) singularities off the origin.
