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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?

 Apr 22, 2021
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The smallest positive integer =3 * 5 ==15, so that:

 

2^2 . 3^4 . 4^4 . 5^6 . 6^6 ==60,466,176,000,000 is a perfect square. Its sqrt =7,776,000

 Apr 22, 2021

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