Three pairs of different positive integers sum to 126, what is the maximum value of the sum of their greatest common divisors.
三个两两不同的正整数，和为126，则它们两两最大公约数之和的最大值为多少．
<gadget id="calculator">18 + 18 + 36</gadget>
<output>72</output>

<result>72</result>