Question 73

Let $$x$$ be the least number divisible by 8, 12, 30, 36 and 45 and $$x$$ is also a perfect square. What is the sum of the digits of the value of x?

Solution

The LCM of 8, 12, 30, 36, 45 is

LCM = $$2\times\ 2\times\ 2\times\ 3\times\ 3\times\ 5$$...........(i)

As we know, 

For number be a perfect square,

The factor of that number must be in pair of 2.

as seen, 2 and 5 should be multipled in (i) to satisfied the above condition. 

$$\therefore\ x=2\times\ 2\times\ 2\times\ 3\times\ 3\times\ 5\times\ 2\times\ 5=3600$$

Sum of the digits of x = 3 + 6 + 0 + 0 = 9

Hence, Option D is correct. 


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