There are 3 natural numbers, each of which is not divisible by the other two numbers, and the product of any two of them is divisible by the third number. What is the smallest sum of 3 natural numbers satisfying the above conditions?
有3个自然数，其中每一个数都不能被另外两个数整除，而且其中任意两个数的乘积都能被第三个数整除．满足上述条件的3个自然数之和最小是多少？
<gadget id="calculator">2 * 3</gadget>
<output>6</output>

<gadget id="calculator">2 * 5</gadget>
<output>10</output>

<gadget id="calculator">3 * 5</gadget>
<output>15</output>

<gadget id="calculator">6 + 10 + 15</gadget>
<output>31</output>

<result>31</result>