GCF and LCM Calculator: Greatest Common Factor, Least Common Multiple and Prime Factorisation
Greatest common factor, least common multiple and prime factors.
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How this calculator works
Choose how many numbers and enter them.
The calculator finds the GCF with the Euclidean algorithm.
It gives the LCM and the prime factors of each number.
Formulas used
- \gcd(a, b) = \gcd(b, a \bmod b)
- \operatorname{lcm}(a, b) = \frac{ab}{\gcd(a, b)}
Worked example
With the default numbers in the calculator above:
- Greatest common factor (GCF): 12
- Least common multiple (LCM): 5040
- Prime factors of 48: 2^4 x 3
- Prime factors of 180: 2^2 x 3^2 x 5
- Prime factors of 84: 2^2 x 3 x 7
Change the numbers in the calculator to see the full working, every step, for your own case.
Common questions
What is the GCF?
The largest whole number that divides all the numbers exactly. It is also called the highest common factor or greatest common divisor.
What is the LCM?
The smallest number that all the numbers divide into exactly.
How do I find them from prime factors?
The GCF takes each prime the fewest times it appears, and the LCM takes each prime the most times it appears.
Related calculators
Got a question about this? Ask an engineering question and get a plain-language answer with references.
Further reading: Any number theory or arithmetic text (the Euclidean algorithm).
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