Scala, 119114 Bytes
var i =val scalai=scala.io.StdIn.readInt;Stream.from(1).foreach{x=>if(s"${x*i}"(i*x+"").map{_.toInt-48asDigit}.max<2) {print(x);System.exit(0)}} Readable version
var i =val scalai=scala.io.StdIn.readInt Stream.from(1).foreach{ x => if(s"${x*i}"(i*x+"").map{_.toInt-48asDigit}.max < 2max<2) { print(x) System.exit(0) } }