Sign up
LCM calculator →

LCM guide

The Least Common Multiple (LCM) Calculator finds the smallest positive integer divisible by two or more numbers. It uses the GCD identity for lightning-fast computation.

Worked examples

Find the LCM of two numbers

  1. Enter 12, 15.
  2. Click Calculate.
Result: LCM = 60

The multiples of 12 are 12, 24, 36, 48, 60... The multiples of 15 are 15, 30, 45, 60... The smallest shared multiple is 60.

Find the LCM of three numbers

  1. Enter 3, 5, 10.
  2. Click Calculate.
Result: LCM = 30

LCM(3, 5) = 15. Then LCM(15, 10) = 30.

Find the LCM of coprime numbers

  1. Enter 7, 11.
  2. Click Calculate.
Result: LCM = 77

Because 7 and 11 are prime, their LCM is simply their product (7 × 11 = 77).

Tips

  • •Use LCM to find the common denominator when adding fractions.
  • •The LCM is always greater than or equal to the largest number in the set.
  • •The calculator also shows the GCD-product relationship for the first two numbers.

Frequently asked questions

What is the Least Common Multiple (LCM)?
The smallest positive integer that is perfectly divisible by two or more given integers.
How is LCM used in adding fractions?
The denominators must be the same before you can add fractions. The LCM of the denominators gives you the Least Common Denominator.
How is LCM related to GCD?
For any two positive integers a and b, the product of their GCD and LCM equals the product of the numbers: GCD × LCM = a × b.
What is the LCM of coprime numbers?
It is their product. For example, LCM(9, 10) = 90.
Can LCM be negative?
No, the LCM is strictly defined as a positive integer.
What is the LCM of 0 and any number?
It is undefined, because 0 is a multiple of every number, so there is no "smallest" positive multiple. The calculator rejects 0.
If one number is a multiple of the other, what is the LCM?
The LCM is the larger number. For example, LCM(4, 12) = 12.
How does the calculator compute LCM so fast?
It uses the formula LCM(a, b) = (|a × b|) / GCD(a, b), leveraging the highly efficient Euclidean algorithm.
What is the difference between LCM and LCD?
LCD stands for Least Common Denominator. It is exactly the same as the LCM, but specifically used when talking about fractions.
Can I find the LCM of decimals?
No. The LCM is only defined for whole numbers.
What is a real-world use of LCM?
Finding when two recurring events will happen at the same time (e.g., traffic lights that turn green every 12 and 15 seconds will sync every 60 seconds).
Is LCM commutative?
Yes. LCM(a, b) = LCM(b, a).
Is LCM associative?
Yes. LCM(a, LCM(b, c)) = LCM(LCM(a, b), c). This is how the calculator handles three or more numbers.
What is the LCM of two prime numbers?
It is their product. For example, LCM(3, 7) = 21.
What happens if the numbers are very large?
The calculator will show an "Infinity" error if the result exceeds JavaScript’s maximum safe integer limit.
How many numbers can I input?
You can input a comma or space-separated list of any length, though 2 to 4 numbers are typical.
Can the LCM equal one of the numbers?
Yes, if one number is a factor of all the others.
How do you find the LCM manually?
You can list the multiples of each number until you find a match, or use prime factorization and take the highest power of each prime factor.
Open the calculator All guides