Revelation 8:2, “And I saw the seven angels which stood before God; and to them were given SEVEN TRUMPETS.”  Revelation 11:15, “And the seventh angel sounded; and there were great voices in heaven, saying, The kingdoms of this world are become the kingdoms of our Lord, and of his Christ; and he shall reign for ever and ever.”  In reading this, we see that towards the middle of the Tribulation Period there were seven angels that were given seven trumpets.  It is in Revelation 11:15 that we read the seventh, or last, trumpet sounded.  As you say, there are some who believe that this is the ‘last trumpet’ that is referenced in 1 Corinthians 15:51-52, “Behold, I shew you a mystery; We shall not all sleep, but we shall all be changed, In a moment, in the twinkling of an eye, AT THE LAST TRUMP: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed.”  We also read in 1 Thessalonians 4:13-17, “But I would not have you to be ignorant, brethren, concerning them which are asleep, that ye sorrow not, even as others which have no hope. For if we believe that Jesus died and rose again, even so them also which sleep in Jesus will God bring with him. For this we say unto you by the word of the Lord, that we which are alive and remain unto the coming of the Lord shall not prevent them which are asleep. For the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with THE TRUMP OF GOD: and the dead in Christ shall rise first: Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.”

When exactly is the ‘last trump’ that announces the Rapture of the church?  Is it the “same trumpet” as the “7th trumpet” of the book of Revelation?

It is important to see that even the 7th trumpet of Revelation 11 is not the last trumpet that will be sounded.  We read of the Lord’s return to the earth at the end of the Tribulation Period in Matthew 24:29-31, “Immediately after the tribulation of those days shall the sun be darkened, and the moon shall not give her light, and the stars shall fall from heaven, and the powers of the heavens shall be shaken: And then shall appear the sign of the Son of man in heaven: and then shall all the tribes of the earth mourn, and they shall see the Son of man coming in the clouds of heaven with power and great glory. And he shall send his angels WITH A GREAT SOUND OF A TRUMPET, and they shall gather together his elect from the four winds, from one end of heaven to the other.”

Why then is the trump of the Rapture called “the last trump”?  Well, we can see that it does not indicate the absolute last trump.  It must have another significance to it.  Throughout the Bible, trumpets were used as signals to gather people, to set armies on the move, and as part of the worship of God. The trumpet that summons the church is called “the trump of God,” while those in Revelation are angelic trumpets. If we consider this as a summoning trumpet, we can look to the Old Testament for insight into this.  Numbers, chapter 10 gives instruction to Israel about the use of trumpets to call an assembly of the people and to set them in motion. We read in Numbers 10:2-5, “Make thee two trumpets of silver; of a whole piece shalt thou make them: that thou mayest use them for the calling of the assembly, and for the journeying of the camps. And when they shall blow with them, all the assembly shall assemble themselves to thee at the door of the tabernacle of the congregation. And if they blow but with one trumpet, then the princes, which are heads of the thousands of Israel, shall gather themselves unto thee. When ye blow an alarm, then the camps that lie on the east parts shall go forward.” 

I believe we can recognize that the ‘last trump’ in 1 Corinthians 11, was a type of summoning trumpet to call all the Lord’s people to be raptured out of this world and into the presence of the Lord.  This must happen before the beginning of the Tribulation period for the Lord promised ALL His saints in Revelation 3:10, “Because you have kept My command to persevere, I also will keep you from the hour of trial which shall come upon the whole world, to test those who dwell on the earth..” (NKJV)  (408.6)