A very large number x is equal to $2^2 \cdot 3^3 \cdot 4^4 \cdot 5^5 \cdot 6^6$. What is the smallest positive integer that, when multiplied with x, produces a product that is a perfect square?
2^2×3^3×4^4×5^5×6^6
The smallest number==3 x 5 ==15
2^2 x 3^4 x 4^4 x 5^6 x 6^6==60,466,176,000,000
Sqrt(60,466,176,000,000) ==7,776,000
