To find the LCM (Lowest Common Multiple) of the numbers 6, 12, 15, and 30, we can use the method of prime factorization or the division method. Here, we'll use the division method as described in the video transcript.
### Step-by-Step Solution:
1. **List the Numbers**: We have the numbers 6, 12, 15, and 30.
2. **Divide by the Smallest Prime Number**: Start with the smallest prime number, which is 2. Check which numbers are divisible by 2.
- 6 ÷ 2 = 3
- 12 ÷ 2 = 6
- 15 is not divisible by 2, so we write it as is.
- 30 ÷ 2 = 15
- This gives us the new row: 3, 6, 15, 15.
3. **Repeat the Process**: Now, we check again with the smallest prime number that can divide any of the numbers in the new row. The next smallest prime is still 2.
- 3 is not divisible by 2, so we write it as is.
- 6 ÷ 2 = 3
- 15 is not divisible by 2, so we write it as is.
- 15 is not divisible by 2, so we write it as is.
- This gives us the new row: 3, 3, 15, 15.
4. **Continue Dividing**: Now, we use the next smallest prime number, which is 3.
- 3 ÷ 3 = 1
- 3 ÷ 3 = 1
- 15 ÷ 3 = 5
- 15 ÷ 3 = 5
- This gives us the new row: 1, 1, 5, 5.
5. **Final Division**: Now, we can divide by the next smallest prime number, which is 5.
- 1 is not divisible by 5, so we write it as is.
- 1 is not divisible by 5, so we write it as is.
- 5 ÷ 5 = 1
- 5 ÷ 5 = 1
- This gives us the new row: 1, 1, 1, 1.
6. **Collect the Prime Factors**: Now, we collect all the prime numbers we used to divide:
- The prime factors used are: 2, 2, 3, 5.
7. **Calculate the LCM**: Multiply all the prime factors together:
- LCM = 2 × 2 × 3 × 5 = 4 × 3 × 5 = 12 × 5 = 60.
### Final Answer:
The LCM of 6, 12, 15, and 30 is **60**.
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