If your question is whether a 36" rim will fit the same cast center, the answer is maybe. It will if you have the right version of a 36" rim. I'm assuming you have the original centers.
 
Just in case there is some confusion in terminology:

1. Tire - The black rubber part with the treads.
2. Rim - The steel ring that the covers up the open part of the tire.
3. Wheel/Center - The cast steel circle mounted to the tractor axle with 6 large holes in it.

If your tractor has 12.4x38" tires, it has 38" rims. A 36" tire will not fit on a 38" rim.

The only way to mount a 36" tire on an M is with the old original 36" "split rims" which have a removable bead to allow mounting the tire.

If you come across any 36" split rims, DO NOT USE THEM. They are dangerous because the removable bead can blow off, possibly at any time, and maim/kill anyone standing near. They are a museum curiosity only.
 

An M should probably have 13.6-38 tires anyway, and they should be easier to find... very common tire.
 

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