Such a normalization has been adopted in the definitive monograph by Cornea, Lupton, Oprea, and Tanré (see below).
In general it is not easy to compute this invariant, which was initially introduced by Lazar Lyusternik and Lev Schnirelmann in connection with variational problems.
In the modern normalization, the cup-length is a lower bound for the LS-category.
a manifold, the lower bound for the number of critical points that a real-valued function on
could possess (this should be compared with the result in Morse theory that shows that the sum of the Betti numbers is a lower bound for the number of critical points of a Morse function).
The invariant has been generalized in several different directions (group actions, foliations, simplicial complexes, etc.