early 15c., in law, "the senior justices of the peace," whose presence was necessary to constitute a court, from Latin quorum "of whom," genitive plural (masc. and neuter; fem. quarum) of qui "who" (from PIE root *kwo-, stem of relative and interrogative pronouns).
The traditional wording of the commission appointing justices of the peace translates as, "We have also assigned you, and every two or more of you (of whom [quoram vos] any one of you the aforesaid A, B, C, D, etc. we will shall be one) our justices to inquire the truth more fully." The justices so-named usually were called the justices of the quorum.
Meaning "fixed number of members of any constituted body whose presence at a particular meeting is necessary to transact business" is recorded by 1610s.