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From the answer choices, E 18 would be the largest K where 3K is divisible by 30!

If K = 18 (2*3*3) then 3 K = 2*3*3*3 and from 30! we have 27 = 3*3*3 and 2 which is divisible by 30!.

However, 18 is not the largest K where 3K is divisible by 30! There are number larger than 18 where 3K is divisible by 30!, if you think about how many 2 can be reduced from 30! You'll understand...

None of the choices is correct, because the largest factor of 30! wud be 30! itself, and so if i have to find a number k of which 3K is a factor of 30! that number K would be 30!/3 .

So among the choices the given choices 18 is the larget number, so wud go for E.