There are 6 natural numbers that are different from each other and not equal to 0, the sum of any 5 numbers is a multiple of 7, and the sum of any 4 numbers is a multiple of 6. May I ask: What is the smallest sum of these 6 numbers?
有6个互不相同且不为0的自然数，其中任意5个数的和都是7的倍数，任意4个数的和都是6的倍数．请问：这6个数的和最小是多少？
<gadget id="calculator">21 * 6</gadget>
<output>126</output>

<gadget id="calculator">1 + 2 + 3 + 4 + 5</gadget>
<output>15</output>

<gadget id="calculator">42 * 15</gadget>
<output>630</output>

<gadget id="calculator">126 + 630</gadget>
<output>756</output>

<result>756</result>