Shalom Aleichem-Kiddush Levanah

Shalom aleichem Rabbi Lauffer. Thank you for answering my last question. The Rema in O.C. 426:16, regarding the Kiddush Levanah, writes “He should say to his fellow three times ‘Shalom alecha.’ Responding to this is like greeting with it.” Does this mean that if 3 different people wish him shalom aleichem and he responds aleichem shalom to all 3, he doesn’t have to say shalom aleichem to 3 more people? Is it the current custom to say “shalom aleichem” to 3 more people even if one has already responded “aleichem shalom” to three different people? Thanks a lot.