Least Common Multiple (LCM) Calculator
Find the least common multiple of two or more numbers.
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Find the Least Common Multiple (LCM) of a Set of Numbers
Our LCM Calculator quickly finds the least common multiple for a set of numbers using prime factorization and also calculates the Greatest Common Divisor (GCD).
What is an LCM Calculator?
A Least Common Multiple (LCM) Calculator is a tool that determines the smallest positive integer that is a multiple of two or more numbers. It's a fundamental concept in arithmetic and number theory, most famously used to find the least common denominator when adding or subtracting fractions.
How It Works: Prime Factorization Method
This calculator uses the prime factorization method to find the LCM, which is particularly effective for multiple numbers:
- Find Prime Factors: It finds the prime factorization of each number in your set.
- Identify Highest Powers: For each unique prime factor found across all numbers, it identifies the highest power to which that factor is raised.
- Multiply: The LCM is the product of these highest powers of all prime factors.
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 integers. For example, the LCM of 4 and 6 is 12.
How do you calculate the LCM?
One way to calculate the LCM is using the formula: LCM(a, b) = |a * b| / GCD(a, b), where GCD is the Greatest Common Divisor. Another method, used by our calculator, involves finding the prime factorization of each number and multiplying the highest power of each prime factor together.
What is the LCM used for?
The most common use for the LCM is in adding and subtracting fractions. You must find the LCM of the denominators (the least common denominator) before you can perform the operation.
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