Luke

Did Mary actually leave Elizabeth before John was born?

When Mary heard from the angel Gabriel that Elizabeth was in her 6th month of pregnancy, Mary quickly left to join her. As the two greeted and the baby John leaped for joy in her womb, Elizabeth was filled with the Holy Spirit and couldn’t believe Mary would come to her that she exclaimed

Luke 1:42-45 “Blessed are you among women, and blessed is the child you will bear! But why am I so favored, that the mother of my Lord should come to me? As soon as the sound of your greeting reached my ears, the baby in my womb leaped for joy. Blessed is she who has believed that the Lord would fulfill his promises to her!”

After noting the three had all that excitement and gratefulness, we soon read the following verses in an interesting order:

Luke 1:56 Mary stayed with Elizabeth for about 3 months and then returned home.

Luke 1:57-58 When it was time for Elizabeth to have her baby, she gave birth to a son. Her neighbors and relatives heard that the Lord had shown her great mercy, and they shared her joy.

Q: When Mary left to go home, Elizabeth would have been in about her 9th month of pregnancy (6th month + “about 3 months” she stayed). With the author having written verses 56 through 58 in that order, was he saying Mary actually left Elizabeth before John was born?