<PRE><B>Question 1062576</B>
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18&lt;sup&gt;180&lt;/sup&gt; = (2&lt;sup&gt;1&lt;/sup&gt;3&lt;sup&gt;2&lt;/sup&gt;)&lt;sup&gt;180&lt;/sup&gt; = 2&lt;sup&gt;180&lt;/sup&gt;3&lt;sup&gt;360&lt;/sup&gt;

Let N be the least integer power of 12 that is divisible by 18&lt;sup&gt;180&lt;/sup&gt;.

12&lt;sup&gt;N&lt;/sup&gt; = (2&lt;sup&gt;2&lt;/sup&gt;3&lt;sup&gt;1&lt;/sup&gt;)&lt;sup&gt;N&lt;/sup&gt; = 2&lt;sup&gt;2N&lt;/sup&gt;3&lt;sup&gt;N&lt;/sup&gt;

So we divide:

{{{(2^(2N)*3^N)/(2^180*3^360)}}} = 2&lt;sup&gt;(2N-180)&lt;/sup&gt;3&lt;sup&gt;(N-360)&lt;/sup&gt;.

The smallest integers N can be must be just enough to make
sure those powers of 2 and 3 are not negative.

So N-360 = 0 or N = 360, 

(and certainly then 2N-180 = 360-180=180 is not negative.)

So N = 360.

Edwin&lt;/pre&gt;&lt;/b&gt;&lt;/font&gt;&lt;/font&gt;



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