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Least Common Multiple (LCM) Calculator
Calculate the smallest common multiple of two or more numbers with step-by-step solutions and visual representation
Input Numbers
Please enter valid positive integers in all fields.
Result
Least Common Multiple (LCM):
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Enter numbers and click "Calculate LCM" to see the solution steps.
Frequently Asked Questions
What is the Least Common Multiple (LCM)?
The Least Common Multiple (LCM) of two or more integers is the smallest positive integer that is divisible by each of the numbers without a remainder. For example, the LCM of 4 and 6 is 12.
How do you calculate LCM?
LCM can be calculated using several methods:
- Prime factorization method: Factor each number to its prime factors, then take the highest power of each prime factor and multiply them together.
- Division method: Divide the numbers by common prime factors until no common prime factor exists, then multiply all divisors and remaining numbers.
- Using GCD: LCM(a, b) = (a × b) / GCD(a, b)
What is the difference between LCM and GCD?
LCM (Least Common Multiple) is the smallest number that is a multiple of two or more numbers, while GCD (Greatest Common Divisor) is the largest number that divides two or more numbers without a remainder. They are related by the formula: LCM(a, b) × GCD(a, b) = a × b.
Can I calculate LCM for more than two numbers?
Yes, our calculator supports LCM calculation for any number of integers. Simply use the "Add Number" button to include additional numbers in your calculation.
What are some practical applications of LCM?
LCM has many real-world applications including:
- Synchronizing events that repeat at different intervals
- Solving problems involving gears and mechanical systems
- Adding and subtracting fractions with different denominators
- Scheduling recurring events
- Cryptography and computer algorithms