Question

Joe Lucky recently won the California lottery. The amount of money that he won just happens to be the smallest number of cents (other than one cent) that is a perfect square, a perfect cube, and a perfect fifth power. How much money did he actually win?

Answer 1

Joe Lucky won
`2^(30)\text{ cents} = 1073741824 \text{ cents}`.

Explanation:

We are told that Joe Lucky recently won the California lottery. The amount of money that he won just happens to be the smallest number of cents (other than one cent) that is a perfect square, a perfect cube, and a perfect fifth power.

A number is perfect square, perfect cube and a perfect fifth power if it can be expressed as 30th power of a natural number because LCM of 2,3 and 5 is 30.

Since it has to be the smallest number and it cannot be 1, therefore, Joe Lucky won
`2^(30)\text{ cents} = 1073741824 \text{ cents}`.