LCM Calculator
Find the Least Common Multiple (LCM) of two or more numbers. Shows the prime factorisation method step by step.
LCM (Least Common Multiple)
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Prime factorisation
What is LCM Calculator?
The Least Common Multiple (LCM) is the smallest positive integer that is divisible by two or more given numbers. It is used when adding or subtracting fractions with different denominators, scheduling repeating events, and solving problems in number theory.
How to use
- 1 Enter two or more positive integers separated by commas or spaces.
- 2 The LCM appears instantly in the result panel.
- 3 The prime factorization of each input number is shown below to explain how the LCM was derived.
- 4 You can enter as many numbers as you need.
Formula
Example calculation
To find LCM(4, 6, 10): prime factors are 2², 2×3, and 2×5. Take highest powers: 2², 3¹, 5¹. LCM = 4 × 3 × 5 = 60. So 60 is the smallest number divisible by 4, 6, and 10.
Frequently asked questions
What is the LCM used for in fractions?
When adding or subtracting fractions with different denominators, you need a common denominator — the LCM of the denominators is the least common denominator (LCD), which keeps numbers small.
What is the relationship between LCM and GCF?
For two numbers a and b: LCM(a, b) = (a × b) / GCF(a, b). So knowing one helps you find the other quickly.
What is the LCM of two prime numbers?
The LCM of two different prime numbers is simply their product, since they share no common factors. For example, LCM(5, 7) = 35.
Can the LCM ever be smaller than the largest input number?
No. The LCM is always greater than or equal to the largest input number, since it must be divisible by all inputs.
What does it mean if the LCM equals the product of the two numbers?
It means the two numbers are coprime (GCF = 1). Their LCM equals their product because they share no common factors.