Question

Find the least number which is a perfect square and also divisible by 6,15,12

Answer 1

Answer:

The LCM of 6, 15, and 12 is 2×3×5×2 = 60.

prime factorisation of 60 is 60= 2×2 ×3×5.

we see that prime factors 3 and 5 are not in pairs. Therefore 60 is not a perfect square.

In order to get a perfect square, each factor of 60 must be paired. So we need to make pairs of 3 and 5 . Therefore, 60 should be multiplied by 3×5,i.e., 15 .

Hence, the required square number is 60×15

= 900.