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Dernière mise à jour : 1 août 2026
LCM Calculator — Least Common Multiple
Créateurs
Dharmendra SinghRéviseurs
Créateurs
Dharmendra SinghRéviseurs
Quick Answer
The LCM Calculator finds the least common multiple of two or more positive integers by repeatedly applying lcm(a,b) = |a*b|/gcd(a,b), returning the combined LCM and the count of valid numbers used.
Enter two or more positive integers separated by commas, and the calculator returns their least common multiple.
Créateurs
Dharmendra SinghRéviseurs
Créateurs
Dharmendra SinghRéviseurs
Formule
lcm(a, b) = |a x b| / gcd(a, b), extended across the whole list
Où :
- a, b, ...=Positive integers to combine
- gcd(a,b)=Greatest common divisor of a and b
Exemples résolus
Two small numbers
Find the LCM of 4 and 6.
- 1Compute gcd(4,6) = 2
- 2lcm(4,6) = (4x6)/2 = 12
- 3Report the result
Three numbers
Find the LCM of 4, 6, and 8.
- 1Reduce pairwise: lcm(4,6) = 12
- 2lcm(12,8) = 24
- 324 is divisible by 4, 6, and 8
Coprime numbers
Find the LCM of 5 and 7, which share no common factors.
- 1gcd(5,7) = 1
- 2lcm(5,7) = 5x7 = 35
- 3Coprime numbers multiply directly
One number divides another
Find the LCM of 3 and 9.
- 1gcd(3,9) = 3
- 2lcm(3,9) = (3x9)/3 = 9
- 3The larger number is the LCM
Introduction
The LCM Calculator finds the smallest positive integer that every number in your list divides into evenly. It is the go-to tool for adding fractions, scheduling repeating events, and simplifying ratios.
What Is the Least Common Multiple?
The least common multiple (LCM) of two or more integers is the smallest positive number that each of them divides into with no remainder. It is used constantly in fraction arithmetic and cyclical scheduling problems.
LCM is always greater than or equal to the largest input number
LCM(a, 1) always equals a
LCM of two coprime numbers equals their product
How the Calculator Works
The calculator repeatedly applies the identity lcm(a, b) = |a x b| / gcd(a, b) across the full list, computing the greatest common divisor with the Euclidean algorithm at each step.
Numbers are parsed from a comma-separated list
Each value must be a positive whole number
The running LCM is combined pairwise until every input is included
Input Guide
Enter every number you want to combine, separated by commas.
- 1
numbers: comma-separated positive integers, e.g. 4,6,8
Output Guide
The calculator returns the combined LCM and how many valid numbers were used.
- 1
lcm: the least common multiple of all valid numbers
- 2
count: how many valid integers were parsed
How to Use This Calculator
Type two or more positive integers separated by commas, then read the LCM result.
Enter at least two positive integers
Separate each value with a comma
Review the LCM and the count of numbers used
Common Mistakes
Most errors come from missing values or entering non-integer or negative numbers.
Entering only one number
Using decimals or negative numbers
Forgetting commas between values
Practical Uses
The LCM shows up whenever you need a shared cycle length or a common denominator.
Adding or comparing fractions
Scheduling repeating events that must align
Simplifying ratios and gear/tooth problems
Prime Factorization Method
An alternative way to find the LCM is to multiply the highest power of every prime that appears in any of the numbers, which gives the same result as the GCD-based formula.
Factor each number into primes
Take the highest power of each prime across all numbers
Multiply those powers together
FAQ
What does the LCM Calculator compute?
It computes the least common multiple of every positive integer you enter, plus how many valid values were used.
How many numbers can I enter?
You can enter as many comma-separated positive integers as you need; the calculator reduces them pairwise.
What happens if I enter only one number?
The calculator requires at least two numbers and returns an error message asking for more input.
Can I use decimals or negative numbers?
No. Only positive whole numbers are accepted; decimals and negative values return a validation error.
How is LCM different from GCF?
The greatest common factor (GCF) is the largest number that divides every input, while the LCM is the smallest number that every input divides into.
Why is the LCM useful for fractions?
Using the LCM as a common denominator lets you add or compare fractions without changing their value.
What is the LCM of two coprime numbers?
When two numbers share no common factors besides 1, their LCM equals their product.
Is the result always larger than my inputs?
The LCM is always greater than or equal to the largest number entered, and equals it only when that number is a multiple of all the others.