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.
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4,5,6
80, 96, 112
Take your choice from 72 or 96
80 and 100 both qualify.
80