Finding the order of integer n in the multiplicative group of integers mod m

MultiplicativeOrder.scala

import scala.annotation.tailrec
def order(n: Int, m: Int): Option[Int] = {
  @tailrec
  def loop(acc: Int, iters: Int): Option[Int] = {
    (acc % m) match {
      case 0 => None
      case 1 => Some(iters)
      case _ => loop((acc * n) % m, iters + 1)
    }
  }
  loop(n % m, 1)
}

Note, this doesn't terminate if gcd(n,m) > 1. Need to fix this.