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Least Common Multiple Calculator

Find the exact least common multiple of up to 20 whole numbers and audit it through prime exponents.

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Complete guide

LCM calculator for multiple integers with prime-factor audit

Paste 2 to 20 whole numbers. Calculator24 returns the exact least common multiple, successive calculation steps and the highest prime powers required by every input.

Editorial checkSuccessive GCD/LCM identity and prime-exponent audit checked against OpenStax methods.Updated September 10, 2026
LCM keeps the largest required prime powersEvery input must divide the result, so the LCM includes each prime at its highest exponent among the inputs.1Prime factors2Largest exponents3Least common multiple
LCM keeps the largest required prime powersEvery input must divide the result, so the LCM includes each prime at its highest exponent among the inputs.

What least common multiple means

The LCM is the smallest nonnegative integer divisible by every entered integer. It synchronizes repeating cycles and finds common denominators.

Prime-factor method

Factor each number and retain every prime at the largest exponent appearing in any input.

LCM(12,18)=2²×3²=36

GCD relationship

For two nonzero integers, multiplying and dividing by their GCD avoids listing multiples.

LCM(a,b)=|a÷GCD(a,b)×b|

Worked three-number example

12=2²×3, 18=2×3² and 30=2×3×5. Keeping 2², 3² and 5 gives 180.

Zero and negative inputs

Signs do not change divisibility. By the convention used here, any set containing zero has LCM zero.

Practical uses and limits

LCM can align schedules, periodic signals and fraction denominators. Extremely large cycles may be mathematically correct but impractical in a real system.

LCM by prime exponents

The LCM takes the maximum exponent for every prime.
InputPrime factorizationContribution
122²×32² and 3
182×3²
302×3×55
LCM2²×3²×5180

Frequently asked questions

What is the LCM of 12 and 18?

It is 36.

Can I enter more than two numbers?

Yes, up to 20.

Does order change the LCM?

No.

What happens if one number is zero?

This calculator returns zero.

Are negative numbers allowed?

Yes. Their absolute values are used.

How is LCM different from GCF?

LCM is a shared multiple; GCF is a shared divisor.

What to keep in mind

Signs are ignored. If any entered number is zero, the LCM is zero. Each absolute value must be at most one trillion and at most 20 values are accepted.

Results display up to 8 decimal places; exported numbers preserve calculation precision. This is a calculation summary, not an official certificate.

Sources and references

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