In　this　article,　we　investigate　the　effect　of　viscosity　on　the　largest　growth　rate　in　the　linear　Rayleigh-Taylor　(RT)　instability　of　a　three-dimensional　nonhomogeneous　incompressible　viscous　flow　in　a　bounded　domain.　By　adapting　a　modified　variational　approach　and　careful　analysis,　we　show　that　the　largest　growth　rate　in　linear　RT　instability　tends　to　zero　as　the　viscosity　coefficient　goes　to　infinity.　Moreover,　the　largest　growth　rate　increasingly　converges　to　one　of　the　corresponding　inviscid　fluids　as　the　viscosity　coefficient　goes　to　zero.　Applying　these　analysis　techniques　to　the　corresponding　viscous　magnetohydrodynamic　fluids,　we　can　also　show　that　the　largest　growth　rate　in　linear　magnetic　RT　instability　tends　to　zero　as　the　strength　of　horizontal　(or　vertical)　magnetic　field　increasingly　goes　to　a　critical　value.　©　2016　Author(s).