the number nearest to 10000 which is exactly

The number nearest to 10,000 that is exactly divisible by each of 3, 4, 5, 6, 7, and 8 is 10,080. This number is the closest multiple of the least common multiple (LCM) of these numbers to 10,000. The LCM of 3, 4, 5, 6, 7, and 8 is 840, and the multiples near 10,000 are 9,240 and 10,080, with 10,080 being closer to 10,000. If the divisibility is considered for the numbers 2, 3, 4, 5, 6, and 7, the two nearest numbers to 10,000 divisible by all of these are 9,660 and 10,080. Thus, the closest number exactly divisible by 3, 4, 5, 6, 7, and 8 near 10,000 is 10,080.