Assuming you want a number that is a multiple of all of 4, 6, 9:
It is a multiple of their lowest common multiple.
lcm(4, 6, 9) = 36
So you require a multiple of 36 between 67 and 113:
67 ÷ 36 = 1 r 31 → 1st multiple of 36 > 67 is 2 x 36 = 72
113 ÷ 36= 3 r 5 → last multiple of 36 < 113 is 3 x 36 = 108
→ both 78 and 108 are numbers between 67 and 113 which are multiples of all of 4, 6 & 9.
If not, re-ask being more specific in your requirements.
4,5,6
80, 96, 112
80 and 100 both qualify.
Take your choice from 72 or 96
80
4,5,6
72, 96
72, 96
72 or 108
80, 96, 112
72, 108
The numbers between 67 and 113 that are multiples of 2, 4, and 5 are 80 and 100.
80 and 100 both qualify.
Take your choice from 72 or 96
80
80 and 100 are the only numbers between 67 and 113 that are multiples of 4,5 and 10.
84, 112