Are the passages from Daniel 9:27, 12:7-10, and Matthew 24:15-21 not describing the same "abominable" force of "desolation"?
The word "abomination" is used three times in the book of Daniel (Dan 9:27 (plural), 11:31 and 12:11). The Hebrew word is 8251 in Strong's Exhaustive Concordance:
from 8262; disgusting, i.e. filthy; especially idolatrous or (concretely) an idol; abominable filth (idol, -ation), detestable (thing).
For 8262 it says:
a primitive root; to be filthy, i.e. (intensively) to loathe, to pollute:- abhor, make abominable, have in abomination, detest, * utterly.
The word is used in the singular in 1 Kings 11:5, 11:7 (twice), 2 Kings 23:13 (three times).
From these texts it can be seen that an "abomination" is (not a force, but) a disgusting idol, or detestable false god.
So where an abomination is said to "stand in the holy place" it is most likely a statue/idol representing a false god or an alter to a false god (Matt 24:15).
As others have already said, an alter was built to Zeus in the Temple in Jerusalem by Antiochus IV Epiphanes: this lead to rebellion by the Jews against the Seleucids and this rebellion lead to Jewish independence under the Hasmonians/Maccabees, a "golden age" of Jewish independence. The action of Antiochus Epiphanes accounts for the mention of abomination of desolation in Daniel 11:31.
When our Lord speaks of the abomination in Matthew 24:15 he must either be speaking of Dan 12:11 or Dan 9:27. In that Daniel 11:31 is referring to exactly the same false god, i.e. Zeus/Jupiter, you could say verse Daniel 11:31 is also being referred to. In other words, what happened in the days of Antiochus Epiphanes with an abomination to Zeus/Jupiter will happen again.
The use in Dan 12:11 seems to be figurative, the main purpose of this section being an encouragement to patience and perseverence in times of trouble. The 1290 days is about three and a half years, a time often used in Scripture to represent a time of chastening/trouble/suffering (James 5:17; Rev 11:2, 12:6, 13:5, 12:14).
The most likely verse Matthew 24:15 refers directly to, probably the only possible verse is therefore Daniel 9:27. If this is true it may have an important impact on our interpretation of Daniel 9:24-27.
Matthew 24 is a difficult passage because it is our Lord's reply to two entirely different questions 1. When will the Temple be destroyed? and 2. When will be the end of the age? (Matt 24:1-3).
I cannot deny that the following interpretation of Matthew 24 has problems, but I think interpretting the abomination of desolation to have appeared at the time of the Temple destruction (AD 70) has much greater problems.. there was no abomination at that time, and there was no desolation either. The following interpretation has both.
Our Lord takes the opportunity to speak of future things in general. One thing must be remembered: our Lord did not know the day of his return to judge the world (Mark 14:32). In his divine nature he knew, but in his human nature he did not know.
He tells them what he does know: the Temple will be destroyed, the abomination of desolation will come, many will rise up claiming to be the Christ, etc. Having finished talking in general about future things he returns to answering their original question (of verse 3): in v34-36 he talks of "these things" and of "that day and that hour". The "these things" in v34 refers back to the destruction of the Temple, and that alone.
On this understanding, the "abomination of desolation" (verse 15) is not necessarily related to the destruction of the Temple (AD 70). It is mentioned in the passage speaking generally of future things. The truth is there is nothing of any historical consequence that happened at the time of the Temple destruction that can be spoken of as the abomination of desolation.
In the days of the Emperor Hadrian about AD 130 a Temple to Jupiter was set up on the site of the Jewish Temple. (In that Jupiter is the same god as Zeus this may also be a clue to the meaning.) This lead to the 3rd Jewish Roman War, the Bar Kokhba Rebellion. Simon Bar Kokhba claimed to be the Messiah (Bar Kokhba, "Son of the Star", a reference to Numbers 24:17). Many Jews, not just in Palestine but in the diaspora, who had rejected Jesus as the Messiah believed Simon Bar Kokhba to be the Messiah: at one time it is said about 400,000 Jewish men were involved in the rebellion, it gained independence for three years. When the Romans finally regained control they were extremely brutal against the Jews, Jerusalem was flattened, and many towns and villages destroyed. Some call the veangence a time not far short of genocide; we are told about half a million Jews were sold into slavery.
The abomination of desolation in Matthew 24 is the Temple to Jupiter set up in the days of Hadrian. The Jews had faith in Simon Bar Kokhba thus demonstrating they had no faith in Jesus of Nazareth and no love for God. They rather hated Jesus (without a cause) and suffered the consequences.
The real cause for the destruction of the Jews was their rejection of Jesus our Lord, revealed by their faith in another.