Final answer:
The clock application is the least reliant on event processing as it has a continuous action of time display, unlike alarms, texting, or gaming apps which depend on user interactions.
Step-by-step explanation:
Out of the options provided, the clock application that constantly displays the time of Los Angeles, New York, and London is the least reliant on event processing. A clock application typically performs a singular, continuous action of keeping and displaying time, which generally involves minimal interaction or event-driven behavior from the user. In contrast, applications like alarms, texting, and video games rely heavily on user interactions and the processing of those events, such as adding or removing alarms, sending messages, or playing games.