Consider a right circular cylinder with a height of 12 units and a circumference of 16 units. A right triangle is formed by the height of the cylinder, the circumference of the base, and the diagonal connecting the top of the cylinder to the base along the curved surface. Find the length of the diagonal. Then, determine the least common multiple (LCM) of the lengths of the three sides of this right triangle. Let's think step by step and output the final answer within \boxed{}.
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