Let's find the least square number other than zero which is divisible by 10,15,20and 30.Also let's write the next square number which will be divisible by these number.

Answer 1

To be a perfect square, the number must be factorable into pairs of equal factors
e.g. 144 = 2x2 x 2x2 x 3x3

10 = 2x5
15 = 3x5
20 = 2x2x5
30 = 2x3x5
So the LCM would be 2x2 x 3 x 5
So to pair them up, we will need another 3x5

So the least square divisible by 10,15,20, and 30
= 2x2 x 3x3 x 5x5 = 900

Using the ideas above, what do you think would be the answer to your second part ?