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The greatest number of four digits which is exactly divisible by 24, 36 and 54 is:
9990
9924
9936
9960
$$ 9936 = 12\times 12\times 23\times 3.$$
So, 24,36 and 54 , all of these numbers have the common factors in 9936.
But, numbers in other options don't have common factors.
So, Option C is correct.
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