Question

What is the least perfect square which is divisible by each 21,36and66​

Answer 1

Answer:

3is the least perfect square for all these numbers

Answer 2

ANSWER IN SHORT WAY :-

L.C.M. of 21, 36, 66 = 2772.

Now, 2772 = 2 x 2 x 3 x 3 x 7 x 11

To make it a perfect square, it must be multiplied by 7 x 11.

So, required number

= 2^2 x 3^2 x 7^2 x 11^2

= 213444

ANSWER IN LONG WAY:-

So,

21 = 3*7

36 = 2*2*3*3

66 = 2*3*11

Let the required number be x.

So x has to have each of these number in a multiple of 2 to be a perfect square.

The Least Common Multiple (the smallest number divisible by these 3 integers) is 2772.

Now, 2772 = (3*3) * 7 * (2*2) * 11

So, for x to be a perfect square, there has to be an even number of 7 and 11.

3 and 2 already appear an even number of times.

So, x = 2772 * 7 * 11

=> x = 213444 (perfect square - 462*462)