“When they had sung
They went out
To the Mount of Olives.”
Καὶ ὑμνήσαντες ἐξῆλθον εἰς τὸ ὄρος τῶν Ἐλαιῶν.
This is exactly word for word in Mark, chapter 14:26, and similar in Luke, chapter 22:39. Both Matthew and Mark agree that after they had sung the praise hymns (Καὶ ὑμνήσαντες), they went out to the hill or the Mount of Olives (ἐξῆλθον εἰς τὸ ὄρος τῶν Ἐλαιῶν). The hymns that they would have sung would be the Hallel Psalms 115-118, that were usually associated with the Passover service. The Mount of Olives was about 2 miles east of the old city of Jerusalem, where many people had been buried for thousands of years. Thus, when Jesus and his 12 disciples had finished with their Passover hymn singing of the Hallel psalms, they went outside the city about 2 miles to this graveyard where there was a hill with a lot of olive trees on it.