What is meant by "the times of the gentiles" in Luke 21:24?

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To what does Luke refer, when he records Jesus’ phrase: “the times of the gentiles” (Luke 21:24)?

Young’s Literal Translation renders the verse in question as follows:

“and they shall fall by the mouth of the sword, and shall be led captive to all the nations, and Jerusalem shall be trodden down by nations, till the times of nations be fulfilled.”

The Apostle Paul makes allusion to something called the “fullness of the Gentiles” in the following passage.

Rom 11:25-27 (NASB)
²⁵ For I do not want you, brethren, to be uninformed of this mystery—so that you will not be wise in your own estimation—that a partial hardening has happened to Israel until the fullness of the Gentiles has come in; ²⁶ and so all Israel will be saved; just as it is written,

 “The Deliverer will come from Zion,   
  He will remove ungodliness from Jacob.”   
  27 “This is My covenant with them,   
  When I take away their sins.”

But are the two expressions related? My understanding is that “the times of the Gentiles” has to do with the fall of Jerusalem in AD 70 (Luke 21:20) as a precursor of a future time of tribulation (Rev 19:19).

But is that a reasonable or legitimate interpretation?