<PRE><B>Question 814037</B>
&lt;pre&gt;
19845k = 3*3*3*3*5*7*7k = 3&lt;sup&gt;4&lt;/sup&gt;*5&lt;sup&gt;1&lt;/sup&gt;*7&lt;sup&gt;2&lt;/sup&gt;k

by a value that will make it
a perfect cube, we much choose a value that will cause
every factor to have an exponent which is a multiple of 3.

The 3&lt;sup&gt;4&lt;/sup&gt; must be multiplied by 3&lt;sup&gt;2&lt;/sup&gt; so it
will become 3&lt;sup&gt;6&lt;/sup&gt; 

The 5&lt;sup&gt;1&lt;/sup&gt; must be multiplied by 5&lt;sup&gt;2&lt;/sup&gt; so it
will become 5&lt;sup&gt;3&lt;/sup&gt;

The 7&lt;sup&gt;2&lt;/sup&gt; must be multiplied by 7&lt;sup&gt;1&lt;/sup&gt; so it
will become 7&lt;sup&gt;3&lt;/sup&gt;


So we must multiply 3&lt;sup&gt;4&lt;/sup&gt;*5&lt;sup&gt;1&lt;/sup&gt;*7&lt;sup&gt;2&lt;/sup&gt; by
3&lt;sup&gt;2&lt;/sup&gt;*5&lt;sup&gt;2&lt;/sup&gt;*7&lt;sup&gt;1&lt;/sup&gt;

So k = 3&lt;sup&gt;2&lt;/sup&gt;*5&lt;sup&gt;2&lt;/sup&gt;*7&lt;sup&gt;1&lt;/sup&gt; = 9*25*7 = 1575

So the smallest possible positive integer value of k is 1575

Checking:

19845*1575 = 31255875 = 315ł 

Edwin&lt;/pre&gt;</PRE>