Question
What is the least common multiple of 120 and 80?
120
240
40
1200
120
240
40
1200
Answers
GPT-4o mini
To find the least common multiple (LCM) of 120 and 80, we can follow these steps:
1. **Find the prime factorization of each number.**
- For 120:
\( 120 = 2^3 \times 3^1 \times 5^1 \)
- For 80:
\( 80 = 2^4 \times 5^1 \)
2. **Identify the highest power of each prime factor present in both factorizations.**
- For \(2\): The highest power is \(2^4\) (from 80).
- For \(3\): The highest power is \(3^1\) (from 120).
- For \(5\): The highest power is \(5^1\) (present in both).
3. **Multiply these together to calculate the LCM:**
\[
\text{LCM} = 2^4 \times 3^1 \times 5^1 = 16 \times 3 \times 5
\]
- First calculate \(16 \times 3 = 48\).
- Then calculate \(48 \times 5 = 240\).
Thus, the LCM of 120 and 80 is \( \boxed{240} \).
1. **Find the prime factorization of each number.**
- For 120:
\( 120 = 2^3 \times 3^1 \times 5^1 \)
- For 80:
\( 80 = 2^4 \times 5^1 \)
2. **Identify the highest power of each prime factor present in both factorizations.**
- For \(2\): The highest power is \(2^4\) (from 80).
- For \(3\): The highest power is \(3^1\) (from 120).
- For \(5\): The highest power is \(5^1\) (present in both).
3. **Multiply these together to calculate the LCM:**
\[
\text{LCM} = 2^4 \times 3^1 \times 5^1 = 16 \times 3 \times 5
\]
- First calculate \(16 \times 3 = 48\).
- Then calculate \(48 \times 5 = 240\).
Thus, the LCM of 120 and 80 is \( \boxed{240} \).