Question

Find the least perfect square, which is divisible by each of 21, 36, 66

Answer 1

LCM of 21, 36, 66 is 3^2, 2^2, 7, 11. So the smallest perfect squareshould be 3^2 x 2^2 x 7^2 x 11^2 = 213444.

Answer 2

Here the sq will be divisible by LCM of 21, 36 and 66 and it will also have all the even powers of prime nos. in its prime factorization.

So LCM(21,36,66) = 7*36*11 = 2772

But here powers of 7 and 11 will be odd as 2772 = 7¹ x 11¹ x 2² x 3²

So we need to multiply 2772 with 7 and 11

Thus the required no. = 2772*7*11 = 213444