18. Venus and Earth are at a certain position relative to the Sun at a certain moment. It is known that Venus orbits the Sun in 225 days, and Earth orbits the Sun in 365 days. How many days at least will it take for both planets to return to their original positions simultaneously?
18. Solution: The time required for both planets to return to their original positions must be a common multiple of the time each planet takes to orbit the sun once. To find the least amount of time for them to return to their original positions, we need to find the least common multiple (LCM) of their orbital periods. Since
$$\begin{array}{l}
225=3^{2} \times 5^{2} \\
365=5 \times 73
\end{array}$$

the LCM of $\{225,365\}=3^{2} \times 5^{2} \times 73=16425$.
Answer: The two planets will simultaneously return to their original positions after at least 16425 days.