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:



Cancel the x's


Since  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.

                           
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Answer: 13×8 = 104.

Edwin
 

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