Description
Compute their gcd by exact Euclidean division, then lcm=0 if gcd=0 or (first/gcd)*second otherwise.
Exact integer arithmetic and finite numeric arithmetic have different range limits. A safe integer number is bounded by +/-9007199254740991, while supported decimal-integer text can represent larger values. Division and remainder also need a signed convention: truncating quotients and Euclidean nonnegative remainders can give different results.
Compute their gcd by exact Euclidean division, then lcm=0 if gcd=0 or (first/gcd)*second otherwise.
When to use this tool
Use Lcm Overflow Safe Factor Order when you need this exact stated integer sign, bound, division, comparison, or factor component.
How to use the tool and how it works
- Enter first, second. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read gcd, lcm. Use the output convention below.
Parse nonnegative decimal integers first and second. Compute their gcd by exact Euclidean division, then lcm=0 if gcd=0 or (first/gcd)*second otherwise. Return both as exact decimal strings.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Text; maximum UTF-16 length 8192. Integer syntax: optional + or - and 1-128 decimal digits; leading zeros accepted. Apply the sign restriction above. |
| second | Second | Required. Text; maximum UTF-16 length 8192. Integer syntax: optional + or - and 1-128 decimal digits; leading zeros accepted. Apply the sign restriction above. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| gcd | Gcd | Required. Text; maximum UTF-16 length 8192. |
| lcm | Lcm | Required. Text; maximum UTF-16 length 8192. |
{
"input": {
"first": "12",
"second": "18"
},
"output": {
"gcd": "6",
"lcm": "36"
}
}Limitations and assumptions
- Dividing before multiplication controls intermediate growth, and zero inputs are supported: gcd(0,0)=0 and lcm=0. Negative values are rejected rather than converted to magnitudes.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Alternative or Complementary methods
Use exact decimal-integer tools when the range exceeds safe numeric integers. State the division, remainder, midpoint, and zero convention before combining results from different operations.
References
Similar or alternative tools
- Rational Addition Denominator Lcm Factor
For positive integer first and second compute their gcd by Euclidean remainder, lcm=(first/gcd)*second, and require that lcm remain a positive safe integer.
- Prime Factorization One Exponent Contribution
Trial-divide candidate prime through its square root, reject a composite, then return factor=prime^exponent as exact decimal text.