If the home was built after 1976, the serial number is on the backing plate. This is the piece of steel that runs across the front of the home, and to which the hitch would be attached. The code says the number must be 3/8" in height, and be located on the foremost crossmember, numbers must not be stamped into hitches
or draw members.
They could be covered with rust, or might be be behind skirting, and can difficult to find, but they are there. If you find rust you may need to lightly sand off the oxidation to get a clear view of the numbers.