Least Common Multiple CalculatorFree online math calculator — instant results, no sign-up
LCM of a list of integers.
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About the Least Common Multiple Calculator
The Least Common Multiple Calculator finds the smallest positive integer that is evenly divisible by all numbers in a given list. It is commonly used by students and professionals for finding common denominators in fractions, scheduling recurring cycles, and solving modular arithmetic problems.
- Numbers
- A comma- or space-separated list of two or more non-zero integers (for example, 4, 6, 10).
Formula and method
lcm(a, b) = |a × b| / gcd(a, b) lcm(a, b, c, ...) = lcm(lcm(a, b), c, ...)
- lcm(a, b)Least common multiple of two integers a and b
- gcd(a, b)Greatest common divisor of integers a and b
- |a × b|Absolute value of the product of a and b
The calculator parses the input string into an array of integers and applies an iterative reduction across the list. At each step, it calculates the least common multiple of the accumulator and the next number using the relation between the product and greatest common divisor.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Numbers4, 6, 10
Results
- LCM60
How to use the Least Common Multiple Calculator
- 1Enter a list of integers separated by commas or spaces.
- 2Compute the greatest common divisor (GCD) and least common multiple (LCM) of the first two numbers.
- 3Combine the resulting LCM with the subsequent integer in the list using the pairwise LCM formula.
- 4Repeat through all remaining values to obtain the overall LCM.
Reading your result
The result displays the smallest positive integer divisible by every number in your set without a remainder. For the default inputs 4, 6, and 10, the output 60 indicates that 60 is the lowest value shared across the multiples of all three numbers.
Limitations
The calculator requires non-zero integer values; including zero results in an undefined or zero LCM, and non-integer decimals are not supported. Extremely large numbers may exceed standard 64-bit floating-point integer precision (safe integers up to 2^53 - 1), leading to overflow.
Common questions
What is the difference between LCM and GCF (GCD)?+
The LCM is the smallest shared multiple divisible by all numbers, which is typically greater than or equal to the largest input. The Greatest Common Factor (GCF) is the largest integer that divides into all the numbers without a remainder, which is less than or equal to the smallest input.
Can the LCM of two or more prime numbers be determined directly?+
Yes. Because distinct prime numbers share no common factors other than 1, their LCM is simply their product.
What happens if one of the entered numbers is negative?+
By mathematical definition, the least common multiple is defined as a positive integer, so negative inputs are evaluated using their absolute magnitudes.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.