The Council of the First Presidency
During certain occasions, the Lord Christ took with Him Peter, James, and John - and only them - to witness certain pivotal events in His ministry. Such pivotal events were the raising of the daughter of Jairus, the raising of Lazarus, the events on top of the Mount of Transfiguration, and our Lord's sufferings in the Garden of Gethsemane. The reason the Lord took Peter, James, and John upon the Mount was to ordain them to the Priesthood and give them the Keys that only the First Presidency can exercise. These three able men eventually led the Church and called and ordained new Apostles such as Paul and Barnabas and Matthias. Unfortunately, all Christ's original Apostles were killed, and His Authority taken from the Earth. It was eventually restored under the hands of these same ancient Apostles (Peter, James, and John) upon the heads of Joseph Smith, Junior and Oliver Cowdery near Harmony, Pennsylvania in May or June of 1829. Four years later on 18 March 1833, the Lord organized the First Presidency, then consisting of Joseph Smith, Junior, President; Sidney Rigdon, First Counselor; and Fredrick G. Williams, Second Counselor. The First Presidency at the time of the death of Joseph Smith consisted of Joseph Smith, Sidney Rigdon, and Hyrum Smith. The First Presidency has been subsequently dissolved and reorganized at the death of every Church President since Joseph Smith. The current First Presidency is Thomas S. Monson, President; Henry B. Eyring, First Counselor; and Dieter F. Uchtdorf, Second Counselor.
The Quorum of the Twelve Apostles
During Jesus' mortal ministry (Matt. 10), He organized the first ever Quorum of the Twelve Apostles which consisted of Peter, Andrew, James, Philip, Bartholomew, Thomas, Matthew, James, Lebaeus Thaddaeus, Simon, and Judas. As stated above, this Quorum was all killed off or taken from the Earth by the Lord, thus their Authority going with them. It was reconstituted by the Lord on 14 February 1835 with Thomas B. Marsh, David W. Patten, Brigham Young, Heber C. Kimball, Orson Hyde, William E. McLellin, Parley P. Pratt, Luke S. Johnson, William Smith, Orson Pratt, John F. Boynton, and Lyman E. Johnson as members. As in former dispensations, at the death or excommunication of a member of the Twelve, a new person in called into the Quorum so as to always have twelve. The current Quorum consists of: Boyd K. Packer, L. Tom Perry, Russell M. Nelson, Dallin H. Oaks, M. Russell Ballard, Richard G. Scott, Robert D. Hales, Jeffery R. Holland, David A. Bednar, Quinton L. Cook, D. Todd Christofferson, and Neil L. Andersen. Together, the First Presidency and Quorum of the Twelve Apostles hold and exercise all the Priesthood Keys on the Earth, with the President of the Church the only man authorized to exercise all the keys at one time.
The Quorums of the Seventy
In Acts 6, the Twelve Apostles chose seven able men to assist them in the work of the ministry. The Savior had previously organized a Quorum of Seventy shortly after the organization, empowerment, and sending forth of the Twelve. The Seventy were organized to help the Apostles lead the Church. After the Great Apostasy, the Lord brooded upon Joseph Smith to reorganize the Seventy in the Dispensation of the Fullness of Times. Just two weeks after the formation of the Quorum of the Twelve apostles in 1835, Joseph Smith organized the First Council of the Seventy. One of the original members was Elder George A. Smith, a cousin to Joseph, and only 19 years of age at the time
From 1835 until 1975, the Quorums of the Seventy became so numerous that they eventually became unwieldy, which eventually were put under the supervision of the Stakes of Zion. They were so unwieldy and disorganized, that in 1975, Spencer W. Kimball, then 12th President of the Church, reorganized the First Quorum as a Quorum of General Authority Seventies, with the Stake Seventies remaining under local jurisdiction. By 1986, the Priesthood office of Seventy was no longer a Stake position, but operated Church wide, with the discontinuance of Stake Seventies. Also in 1986, the Second Quorum of the Seventy was constituted, also consisting of General Authorities. Then, in one of the great administrative motions of President Gordon B. Hinckley, he, in 1997, created the Third, Fourth, and Fifth Quorums of the Seventy. Today, the Church has Eight Quorums of the Seventy. With the creation of the Seventies Quorum, the Church can grow as large as ever God wills it, because the Quorums of the Seventy can expand to any number, whereas there will always and only be Twelve Apostles.
Seeing, therefore, that the Lord actually established a Church on the Earth when He was mortal, it stands to reason that His Church on the earth would have His same organization and offices in this dispensation as in former dispensations. To fully know if what we have discussed is true, you, the reader, must read the Book of Mormon, carefully comparing its doctrine with the Bible. If done with a prayer of faith, you will find that the LDS Church is the only true and living Church upon the face of the whole earth. I know this is true, because I have done it. Remember the words of Jesus, "If any man will do [God's] will, he shall know of the doctrine, whether it be of God, or whether I speak of myself" (John 7:17). I bear witness of the Lord's establishment of the Church of Jesus Christ of Latter-day Saints, and that He established no other modern nor ancient Church or religion, save His Church. In the name of Jesus Christ, amen.