According to the New Testament, the Last Supper (on the night before the crucifixion) took place in the Upper Room. This is the place where Jesus is said to have washed the feet of his disciples.
In the same building on Mt. Zion there is a small synagogue commemorating the tradition that this place houses the tomb of King David. As this tomb is not located in the City of David, this is clearly not an authentic tradition.
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