Purpose and steps
GCD & LCM Calculator validates integers separated by commas or spaces before applying the displayed equation. Zero with a nonzero number has that number’s absolute value as GCD; any zero makes LCM zero.
- Find greatest common divisor and least common multiple across a list of integers using the Euclidean algorithm and exact integer arithmetic.
- Enter Integers separated by commas or spaces in the stated format. Baseline values are for reproduction.
- Check the output unit and convention: Read gcd with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input and compare the result. Zero with a nonzero number has that number’s absolute value as GCD; any zero makes LCM zero. All-zero GCD is returned as zero by convention.
Input reference and units
These values reproduce the model’s demonstration. Replace them with your own records or measurements; they are not recommended targets.
On a small screen, swipe the table horizontally to see all columns.
| Parameter | Demonstration value | How to enter it |
|---|---|---|
| Integers separated by commas or spaces | 12, 18, 24 | Enter integers separated by commas or spaces without adding a unit suffix. Scope: Zero with a nonzero number has that number’s absolute value as GCD; any zero makes LCM zero. |
Model-specific method
How this calculator produces its result
GCD & LCM Calculator: gcd(a,b) = gcd(b, a mod b); lcm(a,b) = |a × b| / gcd(a,b). Input definitions: values = Integers separated by commas or spaces. Use the selected convention throughout the calculation.
GCD & LCM Calculator: calculation relationships
Find greatest common divisor and least common multiple across a list of integers using the Euclidean algorithm and exact integer arithmetic. Zero with a nonzero number has that number’s absolute value as GCD; any zero makes LCM zero. All-zero GCD is returned as zero by convention.
Euclid’s algorithm replaces a pair by its divisor and remainder: gcd(30,18)=gcd(18,12)=gcd(12,6)=6. For nonzero integers, the LCM is |18×30|/6=90. GCD helps reduce fractions and LCM finds a common denominator or repeating interval. A zero in the list makes the LCM zero under this tool’s stated convention.
gcd(a,b) = gcd(b, a mod b); lcm(a,b) = |a × b| / gcd(a,b)
- values: Integers separated by commas or spaces. Enter integers separated by commas or spaces without adding a unit suffix. Scope: Zero with a nonzero number has that number’s absolute value as GCD; any zero makes LCM zero.
- Result units: stated beside each output
- Calculation relationship: gcd(a,b) = gcd(b, a mod b); lcm(a,b) = |a × b| / gcd(a,b)
- Supported domain: see the limits below
Worked example
GCD & LCM Calculator baseline input: Integers separated by commas or spaces: 12, 18, 24. Output: GCD = 6; LCM = 72. Substitute these values into the displayed equation to reproduce the result.
Reproduce the default scenario
This reproduces the default inputs in the reference table above; it is not an additional independent example. Displayed rounding may differ from intermediate precision.
- GCD
- 6
- LCM
- 72
Reading results without overstating them
- Read gcd with its stated unit and convention. The default example and the independent worked scenario use different inputs, so compare the assumptions before comparing the numbers.
- Change one input at a time and use the equation to explain the result; do not mix unit, grade-scale, time-zone or rounding conventions across comparisons.
Assumptions and exclusions
- Zero with a nonzero number has that number’s absolute value as GCD; any zero makes LCM zero.
- All-zero GCD is returned as zero by convention.
Sources and content notes
Toolify describes the implemented algorithm and its assumptions. Sources below support the topic or applicable rules; they do not endorse this calculator. Examples are illustrative, and published rules take precedence over simplified estimates.
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