Question 830222
<pre>
Let the side of each square be x, where x is not necessarily a 
positive integer.  However there must be a positive integer N such that
Nx = 13.  And there must be another positive integer M such that Mx=8

And we want these positive integers N and M to be as small as possible.

So we have

Nx = 13
Mx = 8

Dividing equals by equals:

{{{Nx/(Mx)}}}{{{""=""}}}{{{13/8}}}

Cancel the x's
<pre>
{{{N/M}}}{{{""=""}}}{{{13/8}}}

Since {{{13/8}}} is in lowest terms, the smallest
integers N and M can be are N=13 and N=8, so the smallest
number of squares is to cut it up into 1 ft by 1 ft squares.

<u>                           </u>
<u>| | | | | | | | | | | | | |</u>
<u>| | | | | | | | | | | | | |</u>
<u>| | | | | | | | | | | | | |</u>
<u>| | | | | | | | | | | | | |</u>
<u>| | | | | | | | | | | | | |</u>
<u>| | | | | | | | | | | | | |</u>
<u>| | | | | | | | | | | | | |</u>
<u>| | | | | | | | | | | | | |</u>

Answer: 13×8 = 104.

Edwin</pre>