Question

Find the least common multiple of 8 and 10.(1 point)
Responses

80
80

120
120

40
40

60

Answer 1

To find the least common multiple (LCM) of 8 and 10, we can use the prime factorization method:

1. Prime factorization of 8:
\(8 = 2^3\)

2. Prime factorization of 10:
\(10 = 2^1 \times 5^1\)

3. To find the LCM, take the highest power of each prime that appears in the factorizations:
- For the prime 2, the highest power is \(2^3\) (from 8)
- For the prime 5, the highest power is \(5^1\) (from 10)

4. Now, multiply these together to find the LCM:
\(LCM = 2^3 \times 5^1 = 8 \times 5 = 40\)

So, the least common multiple of 8 and 10 is **40**.