The reason airlines, public transit and the armed forces use 24-hour "military" time is to avoid confusion between a.m. and p.m. hours. You can take the same approach with your cell phone's clock settings to avoid accidentally setting your morning alarm at an afternoon hour.
After you make the switch, the time of day displayed in the morning until 12:59 in the afternoon will look the same, but the afternoon hours will switch to display 13:00 (for 1 p.m.) until 23:59 (for the minute before midnight). So when you set an alarm for 6:30, you'll know it'll go off in the morning to get you up and ready on time.
Not on board with a full switch to military time? Here's another tip:
If you want to be able to set alarms in 24-hour time, but keep your smartphone's main clock in the more familiar 12-hour time, install a secondary alarm clock app (like this one for iPhones). You can switch the app's alarm setings to military time, but keep your phone's main clock the same.