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The Quorum of the Twelve Apostles is the quorum with the highest authority in the Church. The Twelve hold the keys of the priesthood to govern the Church along with the Prophet/President of the Church and his two counselors.
The Quorum of the Seventy consists of seventy elders whose purpose it is to assist the prophet and Quorum of the Twelve, to administer the affairs of the Church under their direction, and to be responsible for Church affairs in far flung areas of the world. There is a Presidency of the Seventy, consisting of seven elders, and because of the huge recent growth of the Church, there are added Quorums of Seventy.
Ward and Stake Quorums
High Priests Quorum meets on a ward basis, but its leaders are called by the stake. Since a man must become a high priest in order to serve in a bishopric or stake presidency, most members of high priests quorums are experienced in church service and may be advancing in age.
Within their quorums, men and young men receive lessons on gospel subjects in priesthood classes. They participate in projects for the welfare of the Saints as directed by the bishop, and they organize certain ward activities. They manage the preparedness and self-reliance of the saints in their areas, especially to prepare for possible emergencies. They also perform acts of needed service for individuals and families in need, often through the home teaching program.