Square room

What is the size of the smallest square room, which can be paved with tiles with dimensions of 55 cm and 45 cm?

How many such tiles are needed?

Correct answer:

a =  495 cm
n =  99

Step-by-step explanation:

$$\begin{gathered} x=55\text{cm} \\ y=45\text{cm} \\ 55=5\cdot 11 \\ 45=3^2\cdot 5 \\ LCM(55,45)=3^2\cdot 5\cdot 11=495 \\ a=LCM(x,y)=LCM(55,45)=495\text{cm} \end{gathered}$$

$n=a^2/(x\cdot y)=495^2/(55\cdot 45)=99$

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