The least number by which multiplying to a rational number is obtained will be:

When 3 will be multiplied with √27 it would be 3√27 which is equal to 9√3 which is not rational number.

When √3 will be multiplied with √27 then it would result in √81 which is 9 and a rational number.

When 9 will be multiplied with √27 it would be 9√27 which is equal to 27√3 which is not rational number.

When 3√3 will be multiplied with √27 then it would result in 3√81 which is 27 and a rational number.

Since the number to be multiplied has to be the smallest the correct answer is √3.

So correct answer is B.