That is a common misconception that got started as a misunderstanding of Milton Friedman's (reasonable) money multiplier equation. Banks cannot lend more money than they have - if they could, then you could start a bank and multiply your own money. The money multiplication that banks can do is take the money that party B has received for selling something and loan it back to to party A, who can use it to buy something from party B again.

A zero percent reserve requirement does not lead in all cases to infinite inflation, because banks are also afraid of a default. Bank's desire to avoid defaults adds another fraction to their reserve ratio and limits money multiplication even when the Fed would technically allow it to proceed infinitely.

Another thing you should know is that Fed chairmen have said that Friedman's equation underestimates bank's ability to create money, because in practice the Fed will allow any bank that desires liquidity to borrow it. The Fed, especially post-great-depression, will happily loan banks however much they needed to cover their reserve requirements, meaning that even before the ratio was set at zero, the number of times a single dollar could be spent was decided primarily by a balance of interest rates and fear of defaults.