<span>The most prevelant rumor is that Gatsby got his money through bootlegging (illegal sale of alcohol), which he did through his ties to the mob. Daisy tells Tom at one point, that Gatsby owned a chain of drug stores, and that is how he got rich.</span>
The answer to your question would be the following one:
Cambridge dictionary defines "prevalent" as "existing very common or happening often". As regards "widespread", it states that it means "existing or happening in many places and/or among many people".
With respect to "requisite", Cambridge dictionary states that it is an adjective which means "necessary or needed for a particular purpose". As you can see, "necessary" is part of the definition of "requisite".
Finally, "propagate" is defined as "to spread opinions, lies, or beliefs among a lot of people". As you can see, "spread" is part of the definition of "propagate".
Prevalent: Widespread
Requisite: Necessary
Propagate: Spread
When I think of persuasive I think of someone convincing another person to do something.
Dishearten, daunt, disparage, overawe, deject, depress. Hope this helps!