Find the lowest common multiple (LCM) of 3, 4 and 6.
The Correct Answer and Explanation is:
✅ Correct Answer:
The lowest common multiple (LCM) of 3, 4, and 6 is 12.
🧠 Step-by-Step Explanation:
To find the lowest common multiple (LCM) of three numbers — 3, 4, and 6 — you are looking for the smallest positive number that all three numbers can divide into evenly, without leaving a remainder.
🔢 Method 1: Listing Multiples
Step 1: List a few multiples of each number
- Multiples of 3: 3, 6, 9, 12, 15, 18, 21
- Multiples of 4: 4, 8, 12, 16, 20
- Multiples of 6: 6, 12, 18, 24
Step 2: Identify the smallest common number in all three lists
- The first number that appears in all three lists is 12.
So, the LCM of 3, 4, and 6 is 12.
🔍 Method 2: Prime Factorization
Step 1: Find prime factors
- 3 = 3
- 4 = 2 × 2 = 2²
- 6 = 2 × 3
Step 2: Take the highest power of each prime factor
- Prime factors: 2² and 3
- LCM = 2² × 3 = 4 × 3 = 12
This confirms the result.
📘 Why LCM Is Useful
The LCM is useful in many real-life scenarios such as scheduling, repeating events, or finding common denominators in fractions. For example, if three machines turn on every 3, 4, and 6 minutes respectively, they will all turn on at the same time every 12 minutes. This is because 12 is the earliest time they all align.
✅ Conclusion
The LCM of 3, 4, and 6 is 12. It is the smallest number that is divisible by all three numbers. You can find it using listing or prime factorization. Both lead to the same result.
