I have code p0420 and code p0300

The catalyst efficiency below threshold P0420 still is pointing at a cat conv problem, may have been ok during smog test but not always ok, I would have checked and verify the cat and o2 sensors are ok and if have to replace cat and P0300 goes away so be it. Are you experiencing a misfire? Your post does not say.

As Ray said, the cat will most likely not go away. it was damaged by the missfire and will have to be replaced. the missfires could have been the plugs and wires but could also be injectors or compression. the 171,174 is a lean condition or long terms too high. that is generally from a vacuum leak, low fuel pressure or mass air flow. it is generally never the o2 sensors as they are doing there job and cannot adjust so they ask for help by tripping the engine light. i think a shop performing a real diag is your answer. that way, the guessing goes away and you get pin point answers. Roy