Two circular dials of exactly the same size are mounted on a wall side by side in such a way that their perimeters touch at one point. Dial 1, which is on the left, spins clockwise around its center, and dial 2, which is on the right spins counter clockwise around its center . (Assume that there is no friction at the point of contact between the dials.) Each dial is marked on its perimeter at three points that are at equal distances around the points marked on dial 1 are N, O, and P and the points marked on dial 2 are X, Y, and Z. If points O and Z are just meeting at the point of contact between the dials, and if dial 1 spins at the same speed as dial 2, what is the smallest number of revolutions of each dial that will bring O and Z together again?