Fill the dryer with four to five old towels. Run the dryer on a regular cycle for five minutes to warm it.
Combine 1 tablespoon of a powdered laundry detergent with two to three drops of water in a bowl. Add more drops of water slowly while you stir the solution until a thick paste forms.
Apply the paste to a washcloth and scrub on the smeared gum. Rub the paste over the entire surface of the dryer for best results.
Rinse the paste off the inside of the dryer with clean water. Place four to five damp washcloths inside the dryer and run it through a complete cycle to remove any remaining gum residue.
Remove any lingering gum residue by soaking a fabric softener dryer sheet in hot water. Let the dryer sheet sit on the gum for 15 to 30 minutes. Scrub on the gum with a nonabrasive sponge and rinse the dryer with clean water.