## Task 1 - 110721

Determine all three-digit natural numbers that are simultaneously divisible by 2, 3, 4, 6, 7, 8, 9, 12, and 14!
A number is divisible by 2, 3, 4, 6, 7, 8, 9, 12, and 14 if and only if it is the least common multiple (LCM) of these numbers or a multiple of it. Given

$$
\begin{gathered}
2=2 \quad 3=3 \quad 4=2 \cdot 2 \quad 6=2 \cdot 3 \quad 7=7 \quad 8=2 \cdot 2 \cdot 2 \\
9=3 \cdot 3 \quad 12=2 \cdot 2 \cdot 3 \quad 14=2 \cdot 7
\end{gathered}
$$

the LCM is \(2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 7 = 504\).

The only three-digit natural number divisible by 504 is 504. Therefore, 504 is the only number that meets all the conditions of the problem.