Greatest number of 6 digits is 999999.

Required number must be divisible by the LCM of 24, 15 and 36 i.e., by 360.

Now on dividing six digit greatest number by LCM we get 279 as remainder.

Therefore the greatest number of 6 digits exactly divisible by 24, 15 and 36 = Six digit greatest number – remainder ⇒ 999999 – 279 = 999720