In this note we construct a commutative diagram in filtered Lagrangian Floer homology that involves a product of certain Lagrangian submanifolds. As a corollary, we prove the Künneth formula for Lagrangian Floer homology. We also prove that the Künneth formula for Lagrangian Floer homology lifts through a Lagrangian type of Piunikhin-Salamon-Schwarz map to the Künneth formula for Morse homology.