To find a number greater than 70 but less than 85 that is divisible by both 2 and 9, we first determine the least common multiple (LCM) of these two numbers.
Since:
- The LCM of 2 and 9 is \( 2 \times 9 = 18 \).
Next, we can find multiples of 18 that are in the range (70, 85).
Calculating multiples of 18:
- \( 18 \times 1 = 18 \)
- \( 18 \times 2 = 36 \)
- \( 18 \times 3 = 54 \)
- \( 18 \times 4 = 72 \)
- \( 18 \times 5 = 90 \)
Now we see which of these multiples fall between 70 and 85:
- The multiple \( 72 \) is between 70 and 85.
- The next multiple, \( 90 \), exceeds 85.
Thus, the only number greater than 70 but less than 85 that is divisible by both 2 and 9 is:
72.
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