Problem C

Stargazing

In a distant solar system, four different comets: Hypatia, Fibonacci, Lovelace, and Euclid, passed by the planet Ptolemy in \(2023\). On Ptolemy, it is known that the Hypatia comet appears every \(3\) years, the Fibonacci comet appears every \(6\) years, the Lovelace comet appears every \(8\) years, and the Euclid comet appears every \(15\) years.

When is the next year that all four comets will pass by Ptolemy?

**Themes: **Algebra, Number Sense