Square room

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

How many such tiles is 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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