# Paving - joints

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

Result

n =  13

#### Solution:

$a=18 \ \text{cm} \ \\ b=24 \ \text{cm} \ \\ l=10 \ m=10 \cdot \ 100 \ cm=1000 \ cm \ \\ \ \\ 18=2 \cdot 3^2 \ \\ 24=2^3 \cdot 3 \ \\ LCM(18, 24)=2^3 \cdot 3^2=72 \ \\ \ \\ x=LCM(a,b)=LCM(18,24)=72 \ \text{cm} \ \\ \ \\ n_{1}=l/x=1000/72 \doteq \dfrac{ 125 }{ 9 } \doteq 13.8889 \ \\ n=\lfloor n_{1} \rfloor=\lfloor 13.8889 \rfloor=13$

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