This paper will present a new method of adaptively constructing smoothers based on Local Sensitivity Analysis (LSA) for multigrid methods. The method can be used in the context of both geometric and algebraic multigrid methods. It is suitable for both constant and variable coefficient problems. Furthermore, the method can be applied to systems arising from both scalar and coupled system partial differential equations (PDEs), as well as linear systems not arising from PDEs. The simplicity of the method will allow it to be easily incorporated into existing multigrid codes while providing a powerful tool for adaptively constructing smoothers tuned to the problem.