Paving - joints

We are paving with rectangular pavement 18 cm × 24 cm was placed side by side in height in a row and the second row in width etc. How many times will the joints meet at a distance of 10 m?

Correct answer:

n =  13

Step-by-step explanation:

$$\begin{gathered} a=18\text{cm} \\ b=24\text{cm} \\ l=10\text{m}\to \text{cm}=10\cdot 100\text{cm}=1000\text{cm} \\ 18=2\cdot 3^2 \\ 24=2^3\cdot 3 \\ LCM(18,24)=2^3\cdot 3^2=72 \\ x=LCM(a,b)=LCM(18,24)=72\text{cm} \\ {n}_1=l/x=1000/72=\frac{125}{9}=13\frac{8}{9}\doteq 13.8889 \\ n=\lfloor n_1\rfloor =\lfloor 13.8889\rfloor =13 \end{gathered}$$

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