Condition 83228

Three boys, Ivo, Vlado, and Alan, are reading the same book, with the condition that they will read the same number of pages every day during the entire reading until they finish the book. Ivo reads 18 pages from it every day, Vlado reads 24 pages, and Alan reads 20 pages. Verify if the book has more than 500 pages.

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} 18=2\cdot 3^2 \\ 24=2^3\cdot 3 \\ 20=2^2\cdot 5 \\ LCM(18,24,20)=2^3\cdot 3^2\cdot 5=360 \\ n=LCM(18,24,20)=360 \\ {d}_1=\frac{n}{18}=\frac{360}{18}=20\text{d} \\ {d}_2=\frac{n}{24}=\frac{360}{24}=15\text{d} \\ {d}_3=\frac{n}{20}=\frac{360}{20}=18\text{d} \\ n<500 \\ x=0 \end{gathered}$$

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