find the greatest number of 5 digits exactly divisible by 12,15 and 36.

Here the L.C.M of 12, 15 and 36 = 180
And the largest five number digit is 99999.
Now dividing 99999 by 180 we get 555 as the quotient and 99 as the remainder.
Now, subtracting this remainder from 99999, we get 
99999 - 99 = 99900.
This is the largest number that is divisible by 12, 15 and 36
555×180 = 99900
To check whether 99900 is exactly divisible by 12, 15 and 36:
9990012 = 83259990015 = 66609990036 = 2775
So we can see 99900 is exactly divisible 12, 15 and 36.
Therefore the required  greatest number is 99900.

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51840

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