Find the least possible perfect square number which is exactly divisible by 6, 40, 49 and 75.

Explanation

The required number must be divisible by the given numbers so it can be the LCM or its multiple number.
Now the LCM of 6, 40 , 49 and 75 =`2 xx 2 xx 2 xx 3 xx 5 xx 5 xx 7 xx 7` But the required number is a perfect square Thus the LCM must be multiplied by `2 xx 3` = 6
Thus the required number =`(2 xx 2 xx 2 xx 3 xx 5 xx 5 xx 7 xx 7) xx (2 xx 3) = 2 xx 2 xx 2 xx 2 xx 3 xx 3 xx 5 xx 5 xx 7 xx 7` = 176400.