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?
Here is a question that look similar
https://web2.0calc.com/questions/help-please-asap_31
I hope this helps!
2^2 * 3^3 * 4^4 * 5^5 * 6^6 =
2^2 * 3^3 * (2^2)^4 * 5^5 * 2^6 * 3^6 =
2^2 * 3^3 * 2^8 * 5^5 * 2^6 * 3^6 =
2^16 * 3^9 * 5^5
We need 3 * 5 = 15
