Does the Mormon church own readers digest?

No. The Church of Jesus Christ of Latter-day Saints (commonly called the "Mormon" church) is not associated with Reader's Digest. Reader's Digest is published by the Reader's Digest Association, it is a publically traded company that is not affiliated with any religious organization, although the magazine does tend to have a conservative leaning.

The Church of Jesus Christ of Latter-day Saints does publish some magazines. The magazines currently published by the church are:

The Friend - geared toward children ages 2-12, contains stories and activities promoting moral values (honesty, service, etc), strong families, scripture stories, and basic church doctrines.

New Era - geared toward teens and young adults ages 12-20, contains stories and activities making moral and religious teachings relevant to teens. Unlike the more storybook nature of The Friend, New Era contains a lot of reader-submitted content and articles about applying religious concepts in everyday life.

The Ensign - for adults 18+, content includes user submitted experiences, articles about church history and doctrine, church news, and transcripts of sermons from church leaders.

Liahona - international. For less common languages in the church, content selections from the above three magazines are combined into one publication. Also contains a section of church news for the region in which the language is spoken.