108, 126, 144, 162, 180, 198, 216, 234, 252, 270, 288 and 306, to name a few.
The least three-digit number that is divisible by both 5 and 9 is 135.
2
26.
240
990.
102
888
40*36 = 1440 is divisible (not divisable) by both. It is not the samllest such number, but that was not required by the question.
There are only two smaller 3-digit numbers and both of them have repeated digits.
The one digit number that has the same number of factors as the number six is three. Six's factors are 1, 2, 3, and 6 while three's factors are 1 and 3. Therefore, both numbers have the same number of factors.
To be divisible by both 4 and 9 a number must be a multiple of the Least Common Factor of 4 and 9. The LCM is 36. The first 3 digit number in each hundred that is a multiple of 36 are as follows :- 108, 216, 324, 432, 504, 612, 720, 828 and 900.
Since both of those numbers contains four digits, there are no three-digit numbers between them.