In Utah, as in most places, interstates take priority over US routes which take priority over state routes. Overlaps between equal route types will generally use the mileage of whichever route carries a greater amount of through traffic, is more significant/recognizable, or is clearly set up as the through route. This usually winds up giving the lower numbered route priority anyway but that is not always the case. We have:
I-15/I-80
I-15/I-84
US 6/US 50 - while both routes share the same mileage here, the overlap is inventoried and legislated as part of US 6
US 6/US 89
US 6/US 191
US 40/US 189
US 40/US 191
US 50/US 89
US 89/US 91
US 163/US 191 - 163 is unsigned, but this does exist per UDOT materials
SR 48/SR 68
SR 68/SR 85
SR 118/SR 120
One noteworthy thing is that business loops are entirely unofficial in Utah, and mileposts on them are entirely related to the state or US highway they overlap (or, for the two locally maintained business loops in the state, simply don't exist). This is in contrast to states like Idaho, where business loops are their own thing and their mileage trumps even any US highways they might be concurrent with.