Back of tower: HDMI and VGA outputs
3 identical monitors: DVI and VGA inputs
My old tower had a DVI and VGA output, so I just ran a VGA from one monitor and DVI from the other into a DVI adapter (pictured) which went to the tower. Obviously new tower lacks the DVI so I dont have that option.

Can I get away with this same setup, only adding a DVI to HDMI converter? That would take care of 2 monitors, then I can just run the 3rd VGA straight to the tower. Would this work?