Question

Select all the common denominators for 14
and 710
.

(1 point)
Responses

10

10

20

20

24

24

32

32

40

Answer 1

To find the common denominators for 14 and 710, we first need to find the multiples of each.

The multiples of 14 are:
- 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, ...

The multiples of 710 are:
- 710, 1420, 2130, 2840, ...

Now, we need to identify the common multiples. However, it's easier to determine the least common multiple (LCM).

To find the LCM, we can use the prime factorization method:

**For 14:**
- 14 = 2 x 7

**For 710:**
- 710 = 2 x 5 x 71

To find the LCM, we take the highest power of each prime:
- From 14: 2^1, 7^1
- From 710: 2^1, 5^1, and 71^1

Therefore, the LCM is:
- LCM = 2^1 x 5^1 x 7^1 x 71^1 = 2 x 5 x 7 x 71

Calculating this:
- 2 x 5 = 10
- 10 x 7 = 70
- 70 x 71 = 4970

The least common multiple is 4970, and the common denominators would be multiples of this number.

Since we need to determine if any of the given options are common denominators:
10, 20, 24, 32, 40 are all not multiples of 4970.

Thus, none of the provided answers are common denominators for 14 and 710.