GCD and LCM Calculator
Paste two or more integers to calculate GCD, LCM, factorization rows, and the two-number product relationship used to check divisibility work.
Inputs
2-12 Integers
Outputs
GCD + LCM
Audit
Prime Factors
Live calculator
GCD and LCM inputs
Paste two or more integers to calculate greatest common divisor, least common multiple, prime factors, and the two-number product check.
Supports 2 to 12 integers between -1,000,000,000 and 1,000,000,000.
Greatest common divisor
6
LCM
360
Values read
18, 24, 60
Product check
For two nonzero integers, a x b = GCD(a,b) x LCM(a,b).
Prime factor audit
| Measure | Value | Check |
|---|---|---|
| 18 | 2 x 3^2 | Prime factorization used to audit common and repeated factors. |
| 24 | 2^3 x 3 | Prime factorization used to audit common and repeated factors. |
| 60 | 2^2 x 3 x 5 | Prime factorization used to audit common and repeated factors. |
Method note
The GCD keeps only factors shared by every value. The LCM keeps the highest required power of each prime factor so every entered integer divides the result.
Calculate common divisors and common multiples
Greatest common divisor
Find the largest integer that divides every entered value evenly.
Least common multiple
Find the smallest nonnegative integer that every entered value divides evenly.
Prime factor audit
Check factor powers for every input before trusting the final GCD or LCM.
GCD and LCM rules used on this page
GCD keeps common factors across all values. LCM keeps enough prime powers for each value to divide the result.
Working formulas
Two-number product check
abs(a x b) = GCD(a,b) x LCM(a,b)
This check applies to two nonzero integers.
GCD from prime factors
use the lowest shared prime powers
Only factors present in every value contribute to the GCD.
LCM from prime factors
use the highest required prime powers
Every prime power needed by any value contributes to the LCM.
Symbols
- a, b - integers
- Two values used in the product relationship check.
- GCD - greatest common divisor
- The largest whole number that divides all inputs evenly.
- LCM - least common multiple
- The smallest nonnegative multiple shared by all inputs.
GCD and LCM with factor-level audit rows
Formula steps that can be audited
- Scientific notation shows coefficient, exponent, engineering notation, and e notation.
- Prime factorization keeps expanded and exponent forms visible for checking.
- GCD and LCM outputs include factor rows so common and repeated factors can be inspected.
- Copy and print controls preserve the exact method labels used on the result cards.
Guardrails for integer and notation work
- Integer tools restrict inputs to whole numbers and explain special cases such as negative values.
- LCM calculations return a clear unavailable state if a result would exceed safe integer precision.
- Scientific notation separates ordinary decimal value, power of ten, and engineering multiples of three.
- Related links connect each calculator to the formula library and nearby math workflows.
Divisibility support for math and worksheets
Students
Check notation, factorization, and divisibility work while seeing each formula convention.
Teachers
Create examples for powers of ten, prime factors, common divisors, and common multiples.
Worksheet builders
Print results and method notes for answer keys, examples, and review sheets.
How it works in three quick steps.
Paste integer values
Enter values separated by commas, spaces, semicolons, pipes, or line breaks.
Read GCD and LCM
Use GCD for the largest shared divisor and LCM for the smallest shared multiple.
Audit prime factors
Review each value's prime factors to see which factors are common or repeated.
Save or print GCD and LCM results
Copy result summary
Copy the final answer with formula labels into notes, documents, or worksheets.
Print the page
Print inputs, result cards, method tables, FAQs, and related math links.
Audit method tables
Use the supporting rows to verify powers of ten, factor powers, or divisibility logic.
About this GCD and LCM calculator
Toolarithm's GCD and LCM Calculator is built for divisibility questions involving two or more integers. It accepts pasted values, calculates the greatest common divisor and least common multiple, and shows prime factor rows for each input. The result panel also includes the two-number product relationship when the input list has exactly two values.
The calculator supports fraction reduction, common denominators, scheduling cycles, worksheet construction, and number theory practice. GCD and LCM are simple ideas, but manual mistakes are common when several values have repeated prime factors. Showing factorization rows next to the final answer makes the workflow easier to check and explain.
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