Three consecutive positive integers, the middle one is a perfect square number, the product of such three consecutive positive integers is called "wonderful number". What is the greatest common divisor of all the "beautiful numbers" smaller than 2008?
三个连续正整数，中间一个是完全平方数，将这样的三个连续正整数的积称为"美妙数"．问所有的小于2008的"美妙数"的最大公约数是多少？
<gadget id="calculator">3 * 4 * 5</gadget>
<output>60</output>

<result>60</result>