Mathematics · Algebra

GCF and LCM Calculator

Find the greatest common factor and least common multiple of two whole numbers.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
Greatest common factor6
Least common multiple36

Calculation steps

  1. Apply the Euclidean algorithm to 12 and 18: GCF = 6.
  2. Compute |12 × 18| ÷ 6.
  3. LCM = 36.

Understand GCF and LCM

One idea, three depths

Choose how deeply to explain GCF and LCM

GCF and LCM: Find the greatest common factor and least common multiple of two whole numbers.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using GCF and LCM to answer this question: find the greatest common factor and least common multiple of two whole numbers? Enter First whole number and Second whole number; the calculator shows Greatest common factor. For example: For 12 and 18, GCF = 6 and LCM = 36. The answer tells you Greatest common factor.

Age 15Explain it to a 15-year-oldConnect it to the formula

The GCF captures every shared prime factor, while the LCM contains enough factors to be divisible by both numbers. The rule is LCM(a,b) = |ab| ÷ GCF(a,b). Its input values are First whole number, Second whole number, and the main result is Greatest common factor. For example: For 12 and 18, GCF = 6 and LCM = 36.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated gcf and lcm relation over the valid integer domain stated below. The implemented relation is LCM(a,b) = |ab| ÷ GCF(a,b), evaluated from First whole number, Second whole number to produce Greatest common factor. The GCF captures every shared prime factor, while the LCM contains enough factors to be divisible by both numbers. The GCF divides both inputs; the LCM is divisible by both inputs.

Inputs and valid domain

  • First whole number must be an integer, at least 1.
  • Second whole number must be an integer, at least 1.

Important boundary: The GCF divides both inputs; the LCM is divisible by both inputs.

The formula

LCM(a,b) = |ab| ÷ GCF(a,b)

How the calculator works through it

It substitutes First whole number, Second whole number into the formula and exposes every numerical step above. The main output is Greatest common factor, accompanied by Least common multiple.

Read the result correctly

The Greatest common factor is the direct answer to “find the greatest common factor and least common multiple of two whole numbers.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

For 12 and 18, GCF = 6 and LCM = 36.

Where this model stops being reliable

The GCF divides both inputs; the LCM is divisible by both inputs.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why GCF and LCM works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    GCF and LCM uses LCM(a,b) = |ab| ÷ GCF(a,b). You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

Optional enrichment

Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Use absolute input values.
  2. Repeatedly replace (a,b) by (b,a mod b).
  3. When b becomes zero, a is the greatest common factor.
Python
            from math import gcd
def greatest_common_factor(a: int, b: int) -> int:
    return gcd(a, b)
assert greatest_common_factor(12, 18) == 6
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <stdint.h>
int64_t greatest_common_factor(int64_t a,int64_t b){if(a<0)a=-a;if(b<0)b=-b;while(b){int64_t r=a%b;a=b;b=r;}return a;}
int main(void){assert(greatest_common_factor(12,18)==6);}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <numeric>
long long greatest_common_factor(long long a,long long b){return std::gcd(a,b);}
int main(){assert(greatest_common_factor(12,18)==6);}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · integer arguments in rdi, rsi and rdx

            ; int64_t greatest_common_factor(int64_t a, int64_t b)
global greatest_common_factor
section .text
greatest_common_factor:

    mov rax, rdi
    test rax, rax
    jns .a_ok
    neg rax
.a_ok:
    mov rcx, rsi
    test rcx, rcx
    jns .b_ok
    neg rcx
.b_ok:
    test rcx, rcx
    jz .done
.loop:
    xor rdx, rdx
    div rcx
    mov rax, rcx
    mov rcx, rdx
    test rcx, rcx
    jnz .loop
.done:
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = greatest_common_factor(a, b)
    result = gcd(abs(round(a)), abs(round(b)));
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[a_Integer, b_Integer] := GCD[a, b];
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Algebra and Trigonometry 2e

Read the related free OpenStax mathematics chapters
Cite this book
APA 7
Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
MLA 9
Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
Chicago author-date
Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). GCF and LCM Calculator. MW SysArc Tools. https://math.mwsysarc.com/algebra/gcf-lcm-calculator

MLA 9

MW SysArc. “GCF and LCM Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/algebra/gcf-lcm-calculator. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “GCF and LCM Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/algebra/gcf-lcm-calculator.

Harvard

MW SysArc (2026) ‘GCF and LCM Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/algebra/gcf-lcm-calculator (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_gcf_lcm_2026,
  author = {{MW SysArc}},
  title = {GCF and LCM Calculator},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/algebra/gcf-lcm-calculator},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - GCF and LCM Calculator
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/algebra/gcf-lcm-calculator
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the GCF and LCM do?

Find the greatest common factor and least common multiple of two whole numbers.

How does the GCF and LCM work?

The calculator applies LCM(a,b) = |ab| ÷ GCF(a,b). The GCF captures every shared prime factor, while the LCM contains enough factors to be divisible by both numbers.

What can I learn from the GCF and LCM?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

MW SysArc Certified