Luke 1:56-60

Luke 1:56 (KJB)
And Mary abode with her about three months, and returned to her own house.

Mary had continued her stay with Elisabeth for an additional three months which would have put the time frame of the full nine months for Elisabeth. Mary may have stayed to help out in any way that she could to help Elisabeth. Three months was also the time set by the Jewish doctors back then as the time needed to ascertain as to whether one was with child or not. Once Mary realized that she was carrying the child at that time, she then returned to her own house. There is nothing written as to what happened in the final six months of Mary’s pregnancy until we get to the time of the census where she was just about ready to deliver Jesus.

Luke 1:57 (KJB)
Now Elisabeth's full time came that she should be delivered; and she brought forth a son.

The prediction of Gabriel which he gave to Zacharias in the temple was now fulfilled. She now held in her hands her own son who was prophesied to come. This would also have been a time for great joy in Elisabeth’s life and should remove the reproach which was on her for being a barren woman. No longer can anyone say that she was under the disfavor of God. Her son was also the prophesied forerunner of the Messiah, something other women cannot claim. (Mal 4:5 KJV) Behold, I will send you Elijah the prophet before the coming of the great and dreadful day of the LORD:

Luke 1:58 (KJB)
And her neighbours and her cousins heard how the Lord had showed great mercy upon her; and they rejoiced with her.

Then came all her neighbors and relatives to bring her good tidings when they had heard how the Lord showed great mercy on her by giving her a son but not just any son, the forerunner of the Messiah. She must have told them about the fact of Gabriel’s visit to Zacharias in the temple and how it was prophesied that she would bear a son and now that prophecy was fulfilled. It was a time of great celebration in Elisabeth’s home.

Luke 1:59 (KJB)
And it came to pass, that on the eighth day they came to circumcise the child; and they called him Zacharias, after the name of his father.

From the verse it seems that the circumcision of John did not take place in the temple but in their home. There was two reasons why the baby was circumcised on the eighth day. (Lev 12:2-3 KJV) Speak unto the children of Israel, saying, If a woman have conceived seed, and born a man child: then she shall be unclean seven days; according to the days of the separation for her infirmity shall she be unclean. {3} And in the eighth day the flesh of his foreskin shall be circumcised. First, because the woman was unclean for the first seven days but on the eighth day she was considered clean. Secondly, the coagulants in the blood which prevent a baby from bleeding out is formed on the eighth day. (Gen 17:11-12 KJV) And ye shall circumcise the flesh of your foreskin; and it shall be a token of the covenant betwixt me and you. {12} And he that is eight days old shall be circumcised among you, every man child in your generations, he that is born in the house, or bought with money of any stranger, which is not of thy seed. Circumcision was also a sign of the covenant between Abraham and God. Here is the original command that boys be circumcised on the eighth day. Normally, the baby is named at the time of birth but the custom of naming the baby on the eighth day is first recorded in Luke.

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Luke 1:60 (KJB)
And his mother answered and said, Not so; but he shall be called John.

Elisabeth would no doubt have loved to have her son named after her husband but this was no ordinary situation. They were told that the name of this baby was going to be John. (Luke 1:13 KJV) But the angel said unto him, Fear not, Zacharias: for thy prayer is heard; and thy wife Elisabeth shall bear thee a son, and thou shalt call his name John. So Elisabeth tells them that the name of the baby is going to be John. The name John means “the Lord is gracious” or “the gift or mercy of the Lord.”