This is the 2930th most frequent Polish word.
największym
"Największym" means "the biggest" or "the largest" in English.
Here, "największym" is the instrumental form of the superlative adjective "największy" (the largest), used to describe the predicate relation of "Warsaw being the largest city."
Warszawa jest największym miastem w Polsce.
Warsaw is the largest city in Poland.
In this sentence, "największym" is used as a superlative adjective in its instrumental form, agreeing with the noun "fanem" (fan), to describe the degree to which he is a fan.
On jest największym fanem tego zespołu.
He is the biggest fan of this band.
Here, "największym" is an instrumental superlative adjective, aligning with the noun "pomocnikiem" (assistant), to describe the role that she assumed.