99,600 is the largest 5-digit number that meets both requirements.
99,996
990.
99990
99990
There is no such number. If you have any such number, n, that is divisible by 3 and 5 then n + 15 is larger, and is divisible by both. And you can add another 15 to that number, and then to that, for ever more.
You can continue to generate numbers that are divisible by both 5 and 9 indefinitely. There is no upper limit.
The largest such number is 9990. 9990/2 = 4995, and 9990/5 = 1998.
A three-digit number that is divisible by both three and four must also be divisible by their least common multiple, which is twelve. The smallest three-digit number divisible by twelve is 108, and the largest is 996. Therefore, any three-digit number that is a multiple of twelve, such as 120, 144, or 480, will meet the criteria of being divisible by both three and four.
Any number that is divisible by both 2 and 3 is divisible by 6.
If a number is divisible by both 8 and 11, it will be divisible by 88.
A three-digit number divisible by both 2 and 5 must end with a 0, as this is the only digit that satisfies both conditions. The smallest three-digit number is 100, and the largest is 999. Therefore, any three-digit number that ends in 0, such as 100, 110, or 990, is divisible by both 2 and 5.
999 is divisible by 9, but not by six; the next lower number divisible by 9 is 990, which is also divisible by 6, so that's the answer. Some shortcuts for divisibility: 0 is divisible by any number. If the last digit of a number is divisible by 2, the number itself is divisible by 2. If the sum of the digits of a number is divisible by 3, the number itself is divisible by 3. If the last TWO digits of a number are divisible by 4, the number itself is divisible by 4. If the last digit of a number is divisible by 5, the number itself is divisible by 5. If a number is divisible by both 2 and 3, it is divisible by 6. If the last THREE digits of a number are divisible by 8, the number itself is divisible by 8. If the sum of the digits of a number is divisible by 9, the number itself is divisible by 9. 990: 9+9+0=18, which is divisible by 9, so 990 is divisible by 9. 18 is also divisible by 3, so 990 is divisible by 3, and since 990 ends in 0 it's also divisible by 2, meaning that it's divisible by 6 as well.