The greatest number of 5 digits to be added to 8321 so that the sum will be exactly divisible by 15,20,24,27,3

the greatest number of 5 digits to be added to 8321 so that the sum will be exactly divisible by 15,20,24,27,32 and 36

First, we need to find the LCM of those 5 numbers through prime factorization:
15 = 3 x 5
20 = 2² x 5
24 = 2³ x 3
27 = 3³
32 = 2^5
36 = 2² x 3²

So the LCM is 2^5 x 3³ x 5 = 4320

Now we need to find multiples of 4320 > 8321 + a 5 digit number or ≤ 8321 + 99999 = 108320.

4320 x 2 = 8640
4320 x 3 = 12960
.
:
4320 x 10 = 43200
.
:
4320 x 25 = 108000 the closest number to 108320 without going over with another multiple, so the answer is:
108000 - 8321 = 99679

Least number divisible by 15, 20, 24, 27, 32 and 36 is LCM of these numbers is 4320
next number 4320 × 2 = 8640 IT IS 4 DIGIT
8640 × 3 = 25920
25920 – 8321 = 17599
add 17599 to 8321 so that the number (8321 + 17599 = 25920) divisible by given numbers.
-----

99679.
99679+8321=108000