Question

Determine the number greater than 70 but less than 85 that is divisible by both 2 and 9.(1 point)
Responses

81
81

84
84

78
78

72

Answer 1

To find a number greater than 70 but less than 85 that is divisible by both 2 and 9, we first find the least common multiple (LCM) of the two numbers.

The LCM of 2 and 9 is 18 (since 2 and 9 are relatively prime, their LCM is simply their product: \( 2 \times 9 = 18 \)).

Next, we can list the multiples of 18 within the range of 70 and 85:

- The multiples of 18 are: 18, 36, 54, 72, 90, etc.
- The multiples of 18 that are greater than 70 but less than 85 are just 72.

Now we'll check the options given:

- **81**: Not divisible by 2 (not even).
- **84**: Divisible by both 2 and 9 (84 ÷ 9 = 9.33).
- **78**: Divisible by both 2 (78 ÷ 2 = 39) and 9 (78 ÷ 9 = 8.67).
- **72**: Divisible by both 2 (72 ÷ 2 = 36) and 9 (72 ÷ 9 = 8).

Among the numbers listed (72, 78, 81, and 84), only 72 is the number that is indeed divisible by both 2 and 9 and falls within the specified range.

Therefore, the answer is:
**72**.