We will show that,for "almost" all arithmetic hyperbolic manifolds with dimension > 3,their fundamental groups are not LERF.The main ingredient in the proof is a study of certain graph of groups with hyperbolic 3-manifold groups being the vertex groups.We will also show that a compact irreducible 3-manifold with empty or tori boundary does not support a geometric structure if and only if its fundamental group is not LERF.