The natural method is the cheapest also. A bottle of hydrogen peroxide cost about 88 cents. Mix it with half water in a spray bottle. Spray on all the moldy areas. Don't rinse. You can use a bleach solution instead but it can turn your grout yellow so you may want to use the hydrogen peroxide first. Spraying the grout on a regular basis with peroxide can inhibit mold from growing. Consider keeping a bottle in your shower. Vinegar also works well for mold problems.
If needed, use a toothbrush and scrub the grout . An electric toothbrush gets the job done faster.