Question

The smallest number by which 2646 must be multiplied to obtain a perfect square is

Answer 1

break 2646 into its factors:2646=49*9*6
(9 , 49 are perfect squares but six is not, so multiply six with six )
(49*6*9)*6
=15876 which is a pefect square.
therefore 6 is the smallest no. to be mutiplied

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Answer 2

LCM of 2646 = 2 * 3^2 * 7^2.

Since every other prime factor is in square except 2 and 3.So, 2 * 3 = 6

2646 * 6 = 15876

The square root of 15876 = 126.

So, the smallest number is 6.


Hope this helps!