96
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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.
60 is one of 5 numbers that has 12 arrays.
You can select 12 numbers for the first digit, 11 numbers for the second digit, and 10 numbers for the third digit; so 12*11*10 = 1320 sets of 3 numbers can be made out of 12 different numbers.
Multiple of both 2 and 3 <=> multiple of 6 So require 2 digit multiples of 6. 2*6 = 12 and 16*6=96 So the answer is 16-2+1 = 15