Shall we do a simple units analysis?

Torque - Newton * meter
Force - Newton
Radius - meter
Gear ratio - unitless
rpm - 1 / second

Now, in my formula,

Force_at_wheels = Torque_at_engine * Gear_ratio / Radius,

both sides have units = Newton.

Now, you multiply rpm to the right-hand side, and its units becomes Newton / seconds. I don't know of any meaningful physics concept that has Newton / seconds as units.