The least number by which we multiply to the 11760 , so that we can get a perfect square number:
The least number by which we multiply to the 11760 , so that we can get a perfect square number:
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The least number by which we multiply to the 11760 , so that we can get a perfect square number:
To find the least number by which 11760 must be multiplied to become a perfect square, we first factorize 11760 into its prime factors. This will help us determine which primes and in what quantity are needed to make all exponents even, as a perfect square has even exponents in its prime factorization.
Prime Factorization of 11760
\[11760 = 2^4 \times 3 \times 5^1 \times 7^2\]
A perfect square requires all exponents in its prime factorization to be even. Here, the prime factor \(3\) and \(5\) has an exponent of \(1\) (which is odd).
Finding the Least Number to Multiply
To make the exponent of \(3\) and \(5\) even, we need to multiply 11760 by another \(3\) and \(5\) = \(15\) .
Conclusion
Therefore, the least number by which 11760 must be multiplied to become a perfect square is \(\boldsymbol{15}\).