Which is a common denominator of 14

Question

and 35
?

(1 point)
Responses

9

9

15

15

16

16

20

Answer 1

To find a common denominator of 14 and 35, we need to determine the least common multiple (LCM) of these two numbers.

1. The prime factorization of 14 is \(2 \times 7\).
2. The prime factorization of 35 is \(5 \times 7\).

To find the LCM, we take the highest power of each prime factor:

• The highest power of 2 is \(2^1\).
• The highest power of 5 is \(5^1\).
• The highest power of 7 is \(7^1\).

Now, multiply these together: \[ LCM = 2^1 \times 5^1 \times 7^1 = 2 \times 5 \times 7 = 70. \]

None of the options provided (9, 15, 16, 20) are common denominators of 14 and 35. The correct common denominator is 70, which is not listed among your options.