“The Siege and Destruction of Jerusalem by the Romans Under
the Command of Titus, A.D. 70,” by David Roberts (1796–1864)
A few days before His death and resurrection, Jesus gave this warning in what is known as the Olivet discourse:
When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, (whoso readeth, let him understand:) then let them which be in Judæa flee into the mountains. (Matthew 24:15–16; emphasis added; compare Mark 13:14 and Luke 21:20–21.)
What is this "abomination of desolation"? I will do my best to explain.

Daniel the prophet, who lived six or seven centuries before Christ, foretold this event or phenomena, as Christ indicated in His prophecy:
And arms shall stand on his part, and they shall pollute the sanctuary of strength, and shall take away the daily sacrifice, and they shall place the abomination that maketh desolate. (Daniel 11:31; emphasis added; compare Daniel 9:27; 12:11.)
The abomination that "they shall place" was a pagan idol set up in the temple of Jerusalem, according to the apocryphal book of 1 Maccabees. This book records the invasion of the city by the marauding forces of the Greek king Antiochus Epiphanes in the autumn of 162 BC (approximate):
Now the fifteenth day of the month Casleu [Kislev in the Hebrew calendar], in the hundred forty and fifth year, they set up the abomination of desolation upon the altar, and builded idol altars throughout the cities of Juda on every side; and burnt incense at the doors of their houses, and in the streets. (1 Maccabees 1:54-55.)
This prophecy and its fulfillment also speak of a time when Jerusalem will be compassed and besieged by invading armies, as by the Roman emperor Titus who destroyed city and the temple in 70 AD and in the last days, just before the coming of Christ (compare Joseph Smith—Matthew 1:12 and Joseph Smith—Matthew 1:32).

Jeremiah also spoke of the desolation that will occur because of Israel's abominations, just prior to the Babylonian captivity and destruction of Jerusalem and Solomon's temple in approximately 587–588 BC:
The Lord could no longer bear, because of the evil of your doings, and because of the abominations which ye have committed; therefore is your land a desolation, and an astonishment, and a curse, without an inhabitant, as at this day. (Jeremiah 44:22; emphasis added.)
Ezekiel, a contemporary of Jeremiah, spoke similarly:
Then shall they know that I am the Lord, when I have laid the land most desolate because of all their abominations which they have committed. (Ezekiel 33:29; emphasis added.) 
Modern revelation speaks of the desolation of abomination or wrath of God which will fall upon wicked:
Therefore, tarry ye, and labor diligently, that you may be perfected in your ministry to go forth among the Gentiles for the last time, as many as the mouth of the Lord shall name, to bind up the law and seal up the testimony, and to prepare the saints for the hour of judgment which is to come; that their souls may escape the wrath of God, the desolation of abomination which awaits the wicked, both in this world and in the world to come. Verily, I say unto you, let those who are not the first elders continue in the vineyard until the mouth of the Lord shall call them, for their time is not yet come; their garments are not clean from the blood of this generation. (D&C 88:84–85; emphasis added; see also D&C 84:117.) 
Therefore, the abomination of desolation speaks of at least these three things: (1) the desecration of the holy temple by setting up of an idol in its precincts, (2) Jerusalem being besieged by foreign or invading armies, and (3) a punishment of the wicked.

It has happened before and it will take place again during a siege of Jerusalem that will occur just before Christ at His Second Coming will set His foot upon the Mount of Olives
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