.
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.
Write 120 as the product of prime numbers:
120 = 
.
Take a number which is the product of same primes 
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 = 
= 30.
If you multiply 120 by 30, you will get the perfect square 120*30 = 3600 = 
= 
.
