9960
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999996
The greatest three digit number that is divisible by 7 is 994.
There is no 4-digit number that is divisible by zero.
The greatest 4-digit number that is divisible by 16 is 9984
The integers divisible by those 5 numbers are exactly the multiples of 1008. The largest multiple of 1008 which is still a four-digit number is 9*1008 = 9072.