Question 116
Find a positive integer satisfying the following three clues:
- When multiplied by $2$, it yields a perfect square.
- When multiplied by $3$, it yields a perfect cube.
- When multiplied by $5$, it yields a perfect fifth power.
- When multiplied by $2$, it yields a perfect square.
- When multiplied by $3$, it yields a perfect cube.
- When multiplied by $5$, it yields a perfect fifth power.