  If R is a local ring of dimension n, of a smooth complex variety, and if I is
a zero dimensional ideal in R, then we prove that e(I)\geq n^n/lc(I)^n. Here
e(I) is the Samuel multiplicity along I, and lc(I) is the log canonical
threshold of (R,I). We show that equality is achieved if and only if the
integral closure of I is a power of the maximal ideal. When I is an arbitrary
ideal, but n=2, we give a similar bound involving the Segre numbers of I.
