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The Articles of Faith are a set of simple statements of belief, taken from a letter written by Joseph Smith to explain various aspects of Mormonism to a non-Mormon audience. The church later accepted it as a canonical statement of doctrinal points.
The seventh Article of Faith states:
7 We believe in the gift of tongues, prophecy, revelation, visions, healing, interpretation of tongues, and so forth.
In terms of organization, the Church of Jesus Christ of Latter-Day Saints is highly hierarchical, roughly comparable to the Catholic Church. Basic doctrines are the same everywhere and do not vary from one congregation to another, so this belief is consistent throughout the church.
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In addition to the list given by Paul in 1 Corinthians 12, Moroni 10:8-18 lists a number of the Gifts of the Spirit, and Doctrine and Covenants 46 lists these and others. These are overlapping but not comprehensive lists. It is specified in scripture that every member of the church is entitled to at least one such gift, although there are some who apparently do not recognize or appreciate what their particular strongest gift is, and in others the gift may become dormant or even be withdrawn because of pride, hypocrisy, or unbelief.
Members of the Church of Jesus Christ of Latter Day Saints do believe in all these gifts and that they are present in the Church today. There are accounts of various of them in official church publications, in personal and family histories, in the monthly fast and testimony meetings, and in private conversations among church members. There possibly are more such gifts manifested than spoken of. For one, they are considered often considered sacred, in accordance with Doctrine and Covenants 63:64. For another, those who are most likely to receive or show them are more interested in quietly doing good than in getting attention or credit and are not trying to impress anyone with signs or wonders, in accordance with Doctrine and Covenants 63:7-12.