Matthew and Mark briefly say that after singing a hymn, Jesus and his disciples went out to the Mount of Olives. The detail can seem incidental, but singing praise belonged naturally to Jewish festival worship.
In the Passover setting, the hymn likely reflects psalms traditionally associated with the feast.
Jewish Passover practice came to associate Psalms 113-118, often called the Hallel, with festival praise. These psalms celebrate God's deliverance, steadfast love, and salvation. The Gospel writers do not identify the exact psalm sung, so certainty about the particular verses should be avoided.
The important contextual point is that Jesus' final journey toward Gethsemane begins after an act of communal praise rooted in Israel's worship.
The background gives spiritual texture to a one-line transition. Jesus does not leave the meal in silence; he and his disciples sing before entering the night of betrayal and arrest.
If the Passover Hallel forms the background, themes of deliverance and God's enduring mercy stand in poignant proximity to the suffering that is about to unfold.