📊 LCM Finder
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📌 What is LCM?
The Least Common Multiple (LCM) of multiple numbers is the smallest number that is a multiple of all given numbers.
Example: The LCM of 4, 6, and 8 is 24, since 24 is the smallest number divisible by all.
📌 Methods to Calculate LCM
- Prime Factorization Method: Find the prime factors of each number and multiply the highest powers of all prime factors.
- Listing Multiples Method: List multiples of each number and find the smallest common multiple.
- Division Method: Divide the numbers by common prime factors until only 1s remain, then multiply all divisors.
📌 Examples of LCM Calculations
| Method | Example | Solution |
|---|---|---|
| Prime Factorization | 12, 15 | 12 = 2² × 3, 15 = 3 × 5 → LCM = 2² × 3 × 5 = 60 |
| Listing Multiples | 4, 5 | Multiples: 4 → 4, 8, 12, 16, 20; 5 → 5, 10, 15, 20 → LCM = 20 |
| Division Method | 8, 12 | Divide by 2 → 4, 6 → Divide by 2 → 2, 3 → Multiply: 2 × 2 × 2 × 3 = 24 |
❓ FAQs
Q1: How do I calculate the LCM?
✅ Find the prime factorization of each number and multiply the highest powers of all prime factors.
Q2: What is the difference between LCM and GCD?
✅ LCM is the least common multiple, while GCD is the greatest common divisor of given numbers.
Q3: Can LCM be smaller than the given numbers?
✅ No, LCM is always equal to or greater than the largest number.
Q4: Why is LCM important in real life?
✅ LCM is used in solving problems related to time cycles, arranging schedules, and managing resources efficiently.
Q5: Can I calculate LCM for more than two numbers?
✅ Yes, LCM can be found for multiple numbers by applying the same methods used for two numbers iteratively.