DAr there is a list of coupled frequencys which you will be able to get from Transport Canada so I don't think you need to be super smart just know where to look.
So when you select say 109.20 that is coupled to a UHF frequency the DME uses.
When you selct DME hold it then holds the UHF frequency and allows you to select a VHF freqency without dragging the UHF coupled freqency into the DME unit.
Just like mobile phones they have search modes and power levesl which are then adjusted as required once they have aquired something usefull I presume down the way. So you should get your max emmission when it can't see anything.