Laundry detergent can help to kill mold spores but the molds spores are killed off much better by using both laundry detergent and vinegar to kill the mold spores.
If you're washing clothes that have a little mold on them add the laundry detergent and about a cup of vinegar to the washing machine and let is soak for 30 minutes to an hour and then run the washing machine through a wash cycle.
Bleach also kills mold spores and bleach is really what you want to use to kill mold spores that are in your house.