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LCM Calculator

Find the least common multiple of two or more whole numbers, with prime factors and steps.

Use non-zero whole numbers. Negative values are treated by absolute value.

Status: initial

Results

Awaiting calculation

Multiples and factors

Introduction

The LCM Calculator finds the least common multiple of two or more whole numbers and shows prime factors and calculation steps.

For two numbers, LCM(a,b) = abs(a x b) / GCD(a,b). For more than two numbers, apply the same formula pair by pair.

Formula and method guide

Two-number LCM

LCM(a,b) = abs(a x b) / GCD(a,b)

Use this efficient method when the GCD is known.

Multiple numbers

LCM(a,b,c) = LCM(LCM(a,b), c)

Use this for three or more whole numbers.

Prime factorization

LCM = product of highest prime powers

Use this method when explaining LCM by factors.

Variables

Numbers

The whole numbers used to find the LCM.

LCM

The smallest positive number divisible by every input value.

GCD

The greatest common divisor used in the pairwise formula.

Prime factors

Prime-number building blocks of each input value.

Multiple

A number produced by multiplying another number by a whole number.

FAQs

What does this LCM Calculator do?
It finds the least common multiple of two or more whole numbers.
What does LCM mean?
LCM means least common multiple.
What is the LCM of 12 and 18?
The LCM of 12 and 18 is 36.
What is the LCM of 8 and 14?
The LCM of 8 and 14 is 56.
Can I enter more than two numbers?
Yes. Enter numbers separated by commas, spaces, or line breaks.
Can I enter negative numbers?
Yes. Negative values are treated by their absolute values.
Can I enter zero?
No. This calculator requires non-zero whole numbers.
Can I enter decimals?
No. LCM is defined here for whole numbers.
How is LCM different from GCD?
LCM is the smallest common multiple; GCD is the greatest common divisor.
Why is LCM useful for fractions?
LCM helps find a least common denominator when adding or subtracting fractions.
What is the prime factorization method?
It multiplies the highest powers of all prime factors found in the numbers.
What is the GCD formula for LCM?
For two numbers, LCM(a,b) = abs(a x b) / GCD(a,b).
Does order matter?
No. LCM is commutative, so changing the order does not change the result.
Can the LCM equal one of the numbers?
Yes, if one number is already a multiple of the other numbers.
Is LCM always positive?
Yes. The least common multiple is reported as a positive number.

References

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