Mat 24:15 "Therefore when you see the ABOMINATION OF DESOLATION which was spoken of through Daniel the prophet, standing in the holy place (let the reader understand),
Mar 13:14a "But when you see the ABOMINATION OF DESOLATION standing where it should not be (let the reader understand),
Luk 21:20 "But when you see Jerusalem surrounded by armies, then recognize that her desolation is near.
We have now seen in the text that this is speaking of the Herod's Temple and its destruction until not one stone is left upon another.
"the ABOMINATION OF DESOLATION which was spoken of through Daniel the prophet"(let the reader understand),
What did Dan in 9:27 say about the abomination that will bring about the desolation of the city and Temple?
After Jesus confirms the covenant and is cut off, not for Himself, which causes the animal sacrifice to cease in relevance to God, it will bring about the following;
and for the overspreading of abominations he shall make [it] desolate, even until the consummation,
This is referring back to 9:26.
and the people of the prince that shall come shall destroy the city and the sanctuary; and the end thereof [shall be] with a flood, and unto the end of the war desolations are determined.
The time involved in this overspreading of abominations took place over the next 40 years.
Then Herod's Temple and the Holy city was laid even to the ground as Jesus had said it would, because they did not recognize the day of their visitation.
What had happened in Herod's Temple where the abomination of desolation was actually standing in the Holy Place?
Because this is when their abominations reached it highest point.
Ananus (in 70 AD) stood in the midst of them, and casting his eyes frequently at the temple, and having a flood of tears in his eyes, he said, "Certainly it had been good for me to die before I had seen the house of God full of so many abominations, or these sacred places, that ought not to be trodden upon at random,filled with the feet of these blood-shedding villains;
Also a false High Priest, that had been chosen by casting lots, had been set up and stood in the Holy Place.
At this point the Titus came and surrounded the city, and laid siege, so that no one could enter or leave the city. The war that ensued ultimately ended with the Jews that had survived being taken captive into the nations and then the full destruction of the city and Temple.