Question
The greatest perfect square less than 20000 which is divisible by each of 2,5,7 and 8 is :___
Answer: Option A
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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=23×51×71. So, 280 must be multiplied with a minimum of 21×51×71 i.e. 70 to make it a perfect square.
So, the required number is: 280×70=19600 which is the greatest perfect square less than 20000 satisfying this condition.
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