LCM of multiple numbers

LCM of Multiple Numbers

LCM(a,b,c) = LCM(LCM(a,b),c). The tool applies this iteratively for up to 10 numbers instantly.

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Practical applications of LCM

LCM is used to find the lowest common denominator when adding fractions and to synchronize events with different periods.
E.g. two buses depart every 15 and 20 minutes. The next simultaneous departure is at LCM(15, 20) = 60 minutes.

Examples

Event synchronization

Input: MMC(4, 6, 10)
Expected output: 60

All three cycles align every 60 units.

Common denominator

Input: MMC(3, 4, 5)
Expected output: 60

Denominator to add 1/3 + 1/4 + 1/5.

Full tool FAQ

What is GCD?

GCD (Greatest Common Divisor) is the largest positive integer that divides all numbers in the set without a remainder. For example, GCD(12, 18) = 6.

What is LCM?

What is the relationship between GCD and LCM?

How does the Euclidean algorithm work?

What are practical uses of GCD and LCM?

Does the tool support more than two numbers?

Why is zero not accepted?

What happens if the LCM is very large?

Frequently asked questions

Why does LCM(a,b) × GCD(a,b) = a × b?

Each prime factor appears in a×b exactly once in the GCD and once in the LCM. The relation allows computing LCM from GCD efficiently.

Does this page replace official or professional review?

No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.