Methods and apparatus for welding a component to fill a groove therein. The method entails simultaneously projecting an electric arc and at least first and second laser beams into the groove. The electric arc melts and deposits a filler material in the groove while the first and second laser beams are projected onto opposite first and second walls, respectively, of the groove. The axis of each of the first and second laser beams is oriented at an acute angle relative to the respective wall thereof.