  Given a monomial ideal in a polynomial ring over a field, we define the
LCM-dual of the given ideal. We show good properties of LCM-duals. Including
the isomorphism between the special fiber of LCM-dual and the special fiber of
given monomial ideal. We show the special fibers of LCM-duals of strongly
stable ideals are normal Cohen-Macaulay Koszul domains. We provide an explicit
describing of minimal free resolutions of LCM-duals of strongly stable ideals.
