In this question, we need to find the least integer that, when multiplied by 2940, becomes a perfect square.

Let`s consider each option to determine if it satisfies the given condition:

Option 1: If we multiply 10 by 2940, we get 29400, which is not a perfect square.

Option 2: If we multiply 15 by 2940, we get 44100, which is a perfect square (210^2). Therefore, option 2 is the correct answer.

Option 3: If we multiply 20 by 2940, we get 58800, which is not a perfect square.

Option 4: If we multiply 35 by 2940, we get 102900, which is not a perfect square.

Therefore, the correct answer is option 2, 15. It is the smallest integer that, when multiplied by 2940, results in a perfect square (44100).