How do you figure out which frequency to contact approach on for a class bravo transition?
The example KFCM to KRNH starts under the Class B shelf, in this case you check KFCM's chart supplement, and it says, &quot;MINNEAPOLIS APP/DEP CON 134.7&quot;:



Which also agrees with the sectional (shown below).
Zoom out in the sectional, and you'll note different frequencies to the NW and NE of the Class B, so if you're transitioning through, the frequency will depend on which direction you're coming from.


Minneapolis-St Paul TAC chart via skyvector.com

Definitely don't use liveatc for frequencies, as that's a hobbyist site.
If you're departing during the tower's operating hours, requesting flight following would be more practical. Also, see related:

On a chart, how can I find the frequency for flight following?
Where is flight following available?
Why did the tower at a Class D airport not set me up with flight following on the ground?
Is a VFR flight following request implied when talking to tower and advising them of your intended airport?
How do I contact Flight Service while in flight?