To find a number greater than 70 and less than 85 that is divisible by both 2 and 9, we can start by determining the least common multiple (LCM) of 2 and 9.
The LCM of 2 and 9 is: \[ \text{LCM}(2, 9) = 18 \]
Next, we identify the multiples of 18 that fall within the range of greater than 70 and less than 85.
The multiples of 18 are:
- \(18 \times 1 = 18\)
- \(18 \times 2 = 36\)
- \(18 \times 3 = 54\)
- \(18 \times 4 = 72\)
- \(18 \times 5 = 90\)
From the list, we can see:
- \(72\) is greater than \(70\) and less than \(85\).
- \(90\) is greater than \(85\) and does not fit our criteria.
Therefore, the only number that meets the conditions is: \[ \boxed{72} \]
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