Question

find the greatest number of 6 digits which is exactly divisible by 8,16 and 24

Answer 1

First we need the LCM of 8, 26, and 24:

8 = 2 * 2 * 2

16 = 2 * 2 * 2 * 2

24 = 2 * 2 * 2 * 3

The LCM is like a parts list with enough parts to make 8, 16, and 24.  In this case that list is 2 * 2 * 2 * 2 * 3 because that list has enough parts to make 8, 16, or 24.

2 * 2 * 2 * 2 * 3 = 48

The LCM of 8, 16, and 24 is 48.

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Now what we want is the largest 6 digit number that is divisible by 48.

Let's do 999,999 / 48

999,999 / 48 = 20833.3125

We want whole numbers, so instead of 20833.3125, let's just take 20833 and multiply it by 48:

20833 * 48 = 999984

999,984 is the largest 6 digit number that is divisible by 48, so 999,984 is also the largest 6 digit number that is divisible by 8, 16, and 24.

Answer:  999,984