Question

The greatest perfect square less than 20000 which is divisible by each of 2,5,7 and 8 is :___

Answer 1

The least number that is exactly divisible by 2, 5, 7 and 8 is its LCM which is 280.

Since 280 is not a perfect square, the multiples of 280 are checked for perfect square.

Now, $280=2^3\times 5^1\times 7^1$. So, 280 must be multiplied with a minimum of $2^1\times 5^1\times 7^1$ i.e. 70 to make it a perfect square.
So, the required number is: $280\times 70=19600$ which is the greatest perfect square less than 20000 satisfying this condition.