Map of US highway 12 and family
Map 1 (of 2) below shows the "earliest" US 12 and the routings of its original branch highways:
US 12 is represented by the purple line running from Yellowstone's northeast entrance to Detroit. A couple temporary routings near Miles City MT are shown in red.
US 112 (historic) is the blue line beginning in Detroit. Originally it followed the red line to Elkhart IN - and later beyond that to Rolling Prairie - but for most of its existence it followed the blue line to New Buffalo MI.
US 212 is the red line from Miles City to Willmar MN - note how it connected to US 12 on both ends.
There were numerous changes to US 12 and its branch highways over the years; compare the map above to Map 2 below, which shows "later" routings:
Map 2 (of 2) above shows:
US 12 is the purple line running from Aberdeen WA to Detroit; note how it was rerouted west of Forsyth MT (more on that below).
US 112 (historic) followed the purple line from Detroit to New Buffalo MI, but after I-94 was built across southern Michigan along what was originally US 12 (red line), that designation was changed to follow what used to be US 112, and the US 112 designation was eliminated.
US 212 is the blue line from Edina MN (near Minneapolis) to Yellowstone's northeast entrance. Note that it no longer connects to US 12 at all.
US 312 (historic): at first, when US 12 was rerouted west of Forsyth, US 212 was still routed up to Miles City. So US 312 was commissioned to follow former US 12 from Forsyth to Yellowstone's northeast entrance. But a few years later, US 212 was rerouted west of Broadus, and that designation took over old US 12/old US 312 from Billings to Yellowstone. So the west terminus of US 312 was moved west to Billings. But its east end was also moved west, because it was extended to follow old US 212 to Broadus.