What would the limited test ban treaty and the nuclear non-proliferation treaty eventually do?

Well the goal of both is in essence is the complete nuclear disarmament and the promotion of the safe and non-military application of the nuclear energy.

The Limited Test Ban Treaty prohibited the testing of nuclear weapons anywhere except underground and the the Nuclear Non-Proliferation Treaty led to the end of the spread of nuclear weapons and the states that did not possess nuclear weapons will not acquire them or create them and in exchange the states that do will provide them with the knowledge of the peaceful nuclear technology.