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.
99,600 is the largest 5-digit number that meets both requirements.
99,996
990.
99990
36360 is a 5 digit number that is divisible by both 3 and 9.
The largest such number is 9990. 9990/2 = 4995, and 9990/5 = 1998.
The least three-digit number that is divisible by both 5 and 9 is 135.
9800 The LCM of 25 & 40 is 200, so need the largest multiple of 200 less than 10000. 10000 ÷ 200 = 50 so 49 x 200 = 9800 is the largest 4 digit number divisible by both 25 and 40.
54
2400
27000
108