Question
Least common multiple of 6 5 4
Answers
GPT-4o mini
To find the least common multiple (LCM) of the numbers 6, 5, and 4, we can use the prime factorization method.
1. **Prime Factorization:**
- \( 6 = 2 \times 3 \)
- \( 5 = 5 \) (5 is already a prime number)
- \( 4 = 2^2 \)
2. **Identify the highest powers of all prime factors:**
- The prime factors we have are 2, 3, and 5.
- The highest power of 2 is \( 2^2 \) (from 4).
- The highest power of 3 is \( 3^1 \) (from 6).
- The highest power of 5 is \( 5^1 \) (from 5).
3. **LCM Calculation:**
- LCM = \( 2^2 \times 3^1 \times 5^1 \)
- LCM = \( 4 \times 3 \times 5 \)
- LCM = \( 12 \times 5 \)
- LCM = \( 60 \)
Therefore, the least common multiple of 6, 5, and 4 is **60**.
1. **Prime Factorization:**
- \( 6 = 2 \times 3 \)
- \( 5 = 5 \) (5 is already a prime number)
- \( 4 = 2^2 \)
2. **Identify the highest powers of all prime factors:**
- The prime factors we have are 2, 3, and 5.
- The highest power of 2 is \( 2^2 \) (from 4).
- The highest power of 3 is \( 3^1 \) (from 6).
- The highest power of 5 is \( 5^1 \) (from 5).
3. **LCM Calculation:**
- LCM = \( 2^2 \times 3^1 \times 5^1 \)
- LCM = \( 4 \times 3 \times 5 \)
- LCM = \( 12 \times 5 \)
- LCM = \( 60 \)
Therefore, the least common multiple of 6, 5, and 4 is **60**.