How Many Chest X-rays Are Required To Equal The Maximum Recommended Radiation Dose For The General Public?

X-ray machines now vary enormously in the amount of radiation that they need to produce an image on an x-ray. So giving you a reliably meaningful response is not easy.
If you would get an x-ray from a very old model – one that might still be in use somewhere in the 3rd world – it might be 5 per year, while in a modern western hospital it might be 200 a year. (20 millisieverts per year @ about .1msv / chest xray)
Also, I am not aware of a lifetime ‘recommended dose’ of radiation. There IS a recommended dose per day or per year. So I think you may need to do a bit of research into, perhaps, the radiation dose of an chest x-ray at your local hospital, and become clearer on what time period you want to encompass for your ‘maximum’ recommended dose.