Question: does full moon occur same time around world

Answer: Yes, A full moon is often thought of as an event of a full night's duration. This is somewhat misleading because its phase seen from Earth continuously waxes or wanes (though much too slowly to notice in real time with the naked eye). Its maximum illumination occurs at the moment waxing has stopped. For any given location, about half of these maximum full moons may be visible, while the other half occurs during the day, when the full moon is below the horizon.