What is the least four-digit whole number that is both a perfect square and a perfect cube?
To be both a perfect square and a perfect cube, a number must be a perfect sixth power, since lcm(2, 3) = 6. The smallest perfect sixth power is 1^6 = 1, but that is not a four-digit number. The next smallest perfect sixth power is 2^6 = 64, but that is not a four-digit number either. The next smallest perfect sixth power is 3^6 = 729, which is still not a four-digit number. The next smallest perfect sixth power is 4^6 = 4096, which is the first four-digit perfect sixth power. Therefore, the least four-digit whole number that is both a perfect square and a perfect cube is 4096. 