I wouldn't call the LDS Church Office Building Brutalist, but Salt Lake does, in fact, have three iconic buildings that fit this description.
The Behavorial Science Building on the University of Utah campus.
The MultiEthnic Highrise downtown:
And probably Salt Lake's most known and biggest beast...
The residential tower on State.
Then there is Salt Lake Community College, which is mostly filled with this type...
Much of the University of Utah's campus is brutalist, including the Medical Plaza Towers.
Beyond that, at the mouth of the canyon, the residential high-rises/mid-rises can fit the bill, as well.
So there you have it.