Find the greatest number of 6 digits numbers exactly divisible by 24, 15 and 36.

To find the greatest 6-digit number that is exactly divisible by 24, 15, and 36, we can find the least common multiple (LCM) of these three numbers and then subtract it from 999,999 (the largest 6-digit number).

The LCM of 24, 15, and 36 is the smallest number that is divisible by all three. To find the LCM, we can break down each number into its prime factors:

24 = 2^3 * 3
15 = 3 * 5
36 = 2^2 * 3^2
Now, we take the highest power of each prime factor:

The highest power of 2 is 2^3.
The highest power of 3 is 3^2.
The highest power of 5 is 5.
Now, multiply these highest powers together to find the LCM:

LCM = 2^3 * 3^2 * 5 = 8 * 9 * 5 = 360

So, the LCM of 24, 15, and 36 is 360.

Now, we need to find the greatest 6-digit number that is divisible by 360. To do this, we divide 999,999 (the largest 6-digit number) by 360:

999,999 / 360 ≈ 2777.77 (approximately)

Since we are looking for the greatest 6-digit number, we can round down to the nearest integer, which is 2777.

Now, we multiply 360 by 2777 to find the largest 6-digit number divisible by 360:

360 * 2777 = 998,520

So, the greatest 6-digit number that is exactly divisible by 24, 15, and 36 is 998,520.