Twenty-four identical 1\times1 squares form a 4\times6 rectangle, as shown. A lattice\:point is a point where a horizontal grid line intersects a vertical grid line. A diagonal of this rectangle passes through the three lattice points P,Q and R. When a 30\times45 rectangle is constructed using identical 1\times1 squares, how many lattice points will a diagonal of this rectangle pass through?
Answer Choices
A. 19
B. 16
C. 15
D. 18
E. 12