Question 1035899
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What is the least positive integer k for which 120×k is the square of an integer?
Is there any shortcut to solve this question?
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Sure, it is.


<pre>
Write 120 as the product of prime numbers:

120 = {{{2^3*3*5}}}.

Take a number which is the product of same primes {{{2^i*3^k*5^n}}} and select the indexes i, j and k in a way 
they complement indexes 3, 1 and 5 to nearest even numbers.

So, your number k = {{{2^1*3^1*5^1}}} = 30.

If you multiply 120 by 30, you will get the perfect square 120*30 = 3600 = {{{60^2}}} = {{{2^(3+1)*3^(1+1)*5^(1+1)}}}.
</pre>