Who was pharaoh of Egypt when Joseph Mary and Jesus went there?

Matthew's Gospel says that the young family fled to Egypt and stayed there until Herod died (4 BCE). The Gospel implies that Jesus was born several years before Herod died, so they would have stayed there several years. After his death, they began to return to their home in Bethlehem but, being warned in a dream, turned aside and travelled to Nazareth in Galilee.

Luke's Gospel says they did not stay in Egypt at all. Luke 2:21-39 says that they went immediately to Jerusalem and then returned peacefully to Nazareth in Galilee.