It is known that the sum of the positive integers a and b is 432, and the sum of the least common multiple and the greatest common factor of a and b is 7776. What is the product of a and b?
已知正整数a与b之和为432，a和b的最小公倍数与最大公因数的和为7776，请问a和b的乘积是多少？
<gadget id="calculator">35 + 37</gadget>
<output>72</output>

<gadget id="calculator">432 / 72</gadget>
<output>6</output>

<gadget id="calculator">35 * 6 * 37 * 6</gadget>
<output>46_620</output>

<result>46_620</result>