Find the least number of square tiles that can be paved on the floor whose length is 120m and breadth is 84m:

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answer is D.

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Detailed Solution

Here we have been given a floor 120m long and 84m wide and we need to determine the smallest number of square tiles that can be laid on the floor. To do this, we must first find the side length of each square.
Now the side length of each square will be H.C.F. 120m and 84m. So let's find the H.C.F. of 120 and 84.
We know that H.C.F. of two numbers is the product of their common prime factors. So write 120 and 84 as the product of their primes, we get

⇒ 120 = 2 × 2 × 2 × 3 × 5 ⇒ 84 = 2 × 2 × 3 × 7

We can clearly see that the common factors are 2, 2, and 3. So, taking their product, we get,
H.C.F =

H.C.F = 12
⇒ length of the side of each square = 12m.
Assume this side length as 'a'.
⇒ a = 12 m – (1)
Now we assume that the smallest number of square tiles that can be tiled is 'n'. Therefore, the area of such 'n' square tiles must equal the area of the floor. So if we equate their area, we get,