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Question 19
The dimensions of a floor are $$18\times24$$. What is the smallest number of identical square tiles that pave the entire floor without the need to break any tile?
Solution
We have dimensions : (24*18)
LCM (24,18) =72
HCF ( 24, 18) = 6
Now Area of floor: 432
In order to minimise the number of tiles considering a tile with a dimension equivalent to the HCF, we have the dimension of the tile to 6*6 = 36 units.
A total of $$\frac{432}{36}$$ = 12 tiles are required.
Minimum number of tiles that pave the entire floor :(LCM)^2/Area = 12
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