< 100 Troublesome Problems in arithmetic > Number and application of shape (68)

 Today, we have a problem with numbers and shapes.
Give it a try. : D 

 The answer is at the bottom of this post. 

 The rectangular tiles, each 9 cm in length and 13 cm in length, were arranged in squares, separated by 1cm in length, as shown in the figure below. What's the smallest number of tiles you've arranged? 

 [Answer] 

 Chapter 35 

 Zoom the finished square to the right and to the bottom by 1cm as shown in the figure. 

 Even so, they become square. However, in this larger square, there is a gap of 1 cm between the right and the bottom, respectively. 

 

This is a vertical object.
9+1 = 10 (cm)
Street
13 + 1 = 14 (cm)
The problem is simpler than it is because it is the same as the square of the. 

 So the lowest common multiple is 10 and 14.
10 = 2 x 5, 14 = 2 x 7
Therefore
Minimum common multiple = 2 x 5 x 7 = 70
Become. 

 In the vertical direction from this
70+10 = 7 (Chapter)
In the horizontal direction
70+14 = 5 (Chapter)
The tiles of make a minimum square. 

 The length of one side of the square is
It becomes 70-1 = 69 (cm).