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LCM Calculator
Find the least common multiple of up to 4 numbers with step-by-step solutions
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📚 Examples, Rules & Help
⚡Quick Examples - Try These Calculations
🔍How It Works
Prime Factorization Method
Find the prime factorization of each number by dividing by prime numbers (2, 3, 5, 7, 11, etc.)
Example: 12 = 2² × 3, and 18 = 2 × 3²
Find Highest Powers
Compare the powers of each prime across all numbers and take the maximum power
Example: For 12 and 18, take 2² (highest power of 2) and 3² (highest power of 3)
Multiply Together
Multiply the highest powers: LCM = 2² × 3² = 4 × 9 = 36
This gives you the smallest number that all original numbers divide into evenly
🌍Real-World Applications
➕ Fraction Addition
Finding common denominators when adding fractions
🕐 Scheduling Problems
Finding when events with different cycles will occur together
⚙️ Engineering
Synchronizing gear ratios and mechanical systems
🔄 Pattern Recognition
Finding when periodic events align or repeat together
❓Frequently Asked Questions
What is the difference between LCM and GCD?
LCM is the smallest positive number divisible by all given numbers, while GCD is the largest number that divides all given numbers.
Can I find LCM of more than 4 numbers?
Yes! The same method works for any quantity of numbers. This calculator supports up to 4 numbers for simplicity.
What if one number is a multiple of another?
If one number is a multiple of another, the LCM will be the larger number.
🎯Common Use Cases
➕ Adding Fractions
- • Finding common denominators for fraction addition
- • Simplifying complex fraction operations
- • Converting mixed numbers to improper fractions
- • Solving fraction word problems
🕐 Scheduling & Timing
- • Bus/train schedule coordination
- • Meeting room booking cycles
- • Recurring event planning
- • Work shift rotations
⚙️ Engineering & Design
- • Gear ratio calculations
- • Frequency matching in electronics
- • Pattern design and tiling
- • Manufacturing cycle optimization
💡Calculator Tips & Best Practices
💡LCM vs GCD Relationship
LCM is always greater than or equal to the largest input number, while GCD is always less than or equal to the smallest input number.
📏Coprime Numbers
If numbers share no common factors (coprime), their LCM equals their product. Example: LCM(7,11) = 77.
📝LCM × GCD Formula
For any two numbers a and b: LCM(a,b) × GCD(a,b) = a × b. This is useful for verification.
⭐Prime Factorization Method
Use prime factorization for complex numbers or multiple inputs - it's more systematic than listing multiples.
📚 References & Further Reading
Comprehensive mathematical reference for LCM theory and applications
External Link
Educational resource with examples and practice problems
External Link
Note: These references provide additional mathematical context and verification of the formulas used in this calculator.