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Mathematics
Number Theory
Perfect Squares
What is the least positive integer n such that the product 65n is a perfect square?
1 answer
We prime factorize $65=5\cdot 13$. So in order for the product to be a perfect square, $n$ must be divisible by both 5 and 13. The smallest multiple of $5$ and $13$ is $5\cdot 13=\boxed{65}$.
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