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# Number Theory

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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?

Jan 14, 2022

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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

Jan 14, 2022