Divide the natural numbers from 1 to 30 into two groups such that the product A of all the numbers in the first group is divisible by the product B of all the numbers in the second group. What is the minimum value of ((A)/(B))?
将从1到30的自然数分成两组，使得第一组中所有数的乘积A能被第二组中所有数的乘积B整除．则((A)/(B))的最小值是多少？
<gadget id="calculator">2 * 2 * 2</gadget>
<output>8</output>

<gadget id="calculator">2 * 3 * 3</gadget>
<output>18</output>

<gadget id="calculator">2 * 2 * 5</gadget>
<output>20</output>

<gadget id="calculator">3 * 7</gadget>
<output>21</output>

<gadget id="calculator">2 * 11</gadget>
<output>22</output>

<gadget id="calculator">2 * 2 * 2 * 3</gadget>
<output>24</output>

<gadget id="calculator">5 * 5</gadget>
<output>25</output>

<gadget id="calculator">2 * 13</gadget>
<output>26</output>

<gadget id="calculator">3 * 3 * 3</gadget>
<output>27</output>

<gadget id="calculator">2 * 2 * 7</gadget>
<output>28</output>

<gadget id="calculator">5 * 8 * 17 * 18 * 19 * 20 * 21 * 22 * 23 * 24 * 25 * 26 * 27 * 28 * 29</gadget>
<output>16_903_600_410_977_280_000</output>

<gadget id="calculator">2 * 2</gadget>
<output>4</output>

<gadget id="calculator">2 * 3</gadget>
<output>6</output>

<gadget id="calculator">3 * 3</gadget>
<output>9</output>

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

<gadget id="calculator">2 * 2 * 3</gadget>
<output>12</output>

<gadget id="calculator">2 * 7</gadget>
<output>14</output>

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

<gadget id="calculator">2 * 2 * 2 * 2</gadget>
<output>16</output>

<gadget id="calculator">1 * 2 * 3 * 4 * 6 * 7 * 9 * 10 * 11 * 12 * 13 * 14 * 15 * 16 * 30</gadget>
<output>15_692_092_416_000</output>

<gadget id="calculator">16_903_600_410_977_280_000 / 15_692_092_416_000</gadget>
<output>1_077_205</output>

<result>1_077_205</result>