Question

The least common multiple of 20 and 14 is:
(1 point)
Responses

280
280

20
20

140
140

70

Answer 1

To find the least common multiple (LCM) of 20 and 14, we can use the prime factorization method.

1. Prime factorization:
- 20 = 2^2 × 5
- 14 = 2^1 × 7

2. To find the LCM, take the highest power of each prime factor:
- For the prime factor 2, the highest power is 2^2 (from 20).
- For the prime factor 5, the highest power is 5^1 (from 20).
- For the prime factor 7, the highest power is 7^1 (from 14).

3. Now multiply these together to find the LCM:
LCM = 2^2 × 5^1 × 7^1 = 4 × 5 × 7 = 20 × 7 = 140.

Therefore, the least common multiple of 20 and 14 is **140**.

So the correct response is:
**140**