Suppose the greatest common factor of two numbers is 23, and the quotient of their least common multiple divided by their greatest common factor is 78, then what is the smallest sum of these two numbers?
设两个数的最大公因数是23，它们的最小公倍数被它们的最大公因数除后商是78，那么这两个数的和最小是多少？
<gadget id="calculator">13 + 6</gadget>
<output>19</output>

<gadget id="calculator">23 * 19</gadget>
<output>437</output>

<result>437</result>