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