A RM can be determined from a 1RM, 3RM, 5RM, 10RM....whatever (not necessarily just 10RM).
If you are doing 10 repetitions of an exercise, you should be able to get through all your repetitions in a set but it should be hard work. i.e. if you blow through 10 reps with no difficulty you could increase the weight; if you can't finish your 10 reps you should decrease the weight. It should also be an appropriate work load that after a rest between sets you should be able to get through the all 10 reps again.