Pokémon cards

Leo collects Pokémon cards. Kyle, Issaic, and Dr. Hong look at his card box and then have the following conversation with Leo --

  • Kyle: Leo has at most 65 cards;
  • Issaic: Leo has at least 70 cards;
  • Dr. Hong: Leo has at least 58 cards.

If exactly one of them is false, what’s the smallest number of cards Leo has?