6th grade math help

Question

Russell has tiles that measure 43 centimeters by 49 centimeters. If he wants to arrange them to form the smallest possible square, without cutting or overlapping any of the tiles, how many centimeters long will each side of the square be?How do you work this problem?

Answer 1

Hi Russell.

 

This problem involves finding the Lowest Common Multiple (LCM) of the two numbers, which would give us the number of tiles to join across and the number of tiles to join down to form our smallest square.

 

We can find the LCM by breaking each number down into its prime factors and then multiplying the unique prime factors from each number together:

    49 (prime factors):  7 x 7

    43 (prime factors):  none, since 43 is prime #

 

So our LCM will be 7 x 7 x 43 = 49 x 43 = 2107.

 

Now we can see that we'll need to form each row of 43 tiles across (49 x 43) as well as have 49 of those rows going down (43 x 49) forming our square of 2107 cm (length across) and 2107 cm. (width down).

 

This was a tricky problem in that we first needed to see what we had to find.  The Lowest Common Multiple (LCM) of the dimensions of the rectangle gave us the value we needed for the length of the side of the square.

 

Thanks for submitting this problem and glad to help.

 

God bless, Jordan. 

Answer 2

The problem tells us that each tile is 43 cm by 49 cm.  Also, no cutting or overlapping is allowed.  The result must be the smallest possible square.  What are the dimensions of the square?    [I'm practicing putting the problem in my own words.]

 

I notice that the problem allow us to tilt the tiles.

 

Let's start by finding the prime factors:

     43   =  43

     49   = 7*7

 

No numbers appear as factors of both 43 and 47, so, the LCM (least common multiple) is 43*7*7 = 2107 cm.     (this is the side of the square).