LCM Calculator - Least Common Multiple
Find the Least Common Multiple (LCM) of any numbers using multiple methods. Calculate LCM with prime factorization, multiples listing, and step-by-step solutions.
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Common LCM Examples
4, 6→LCM: 12(2² × 3)
8, 12→LCM: 24(2³ × 3)
6, 9, 15→LCM: 90(2 × 3² × 5)
5, 7→LCM: 35(5 × 7 (coprime))
10, 15, 20→LCM: 60(2² × 3 × 5)
12, 18, 24→LCM: 72(2³ × 3²)
LCM Calculation Methods
Prime Factorization: Take highest power of each prime factor
Listing Multiples: List multiples until you find a common one
GCF Formula: LCM(a,b) = |a×b| / GCF(a,b)
Ladder Method: Divide by common factors systematically
Understanding Least Common Multiple (LCM)
The Least Common Multiple (LCM) is the smallest positive integer that is divisible by all given numbers. It's a crucial concept in mathematics with practical applications in fraction operations, scheduling, and pattern recognition.
Key Concepts:
- Definition: The smallest positive integer divisible by all given numbers
- Multiple: A number that can be divided by another number without remainder
- Common Multiple: A number that is a multiple of all given numbers
- Relationship with GCF: For two numbers: GCF × LCM = Product of the numbers
Calculation Methods:
- Prime Factorization Method: Take the highest power of each prime factor
- Listing Method: List multiples until finding the first common one
- GCF Formula: LCM(a,b) = |a×b| / GCF(a,b) for two numbers
- Ladder Method: Systematic division approach
Real-World Applications:
- Fraction Operations: Finding common denominators for addition and subtraction
- Scheduling and Planning: Determining when recurring events coincide
- Manufacturing: Optimizing production cycles and packaging
- Music and Art: Creating patterns and rhythmic cycles
- Engineering: Gear ratios and mechanical timing systems
Properties and Patterns:
- LCM is always ≥ the largest number in the set
- If numbers are coprime, LCM equals their product
- LCM(a, b, c) = LCM(LCM(a, b), c) for multiple numbers
- LCM and GCF are inversely related for two numbers
Frequently Asked Questions - LCM Calculator
The LCM is the smallest positive integer that is divisible by all given numbers. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 divide into evenly.
Tips
- Enter the dimensions in the same unit for consistency.
- Results update automatically as you type.
- Use the unit selector to convert between different measurement systems.