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Template:LCM
[⧼Purge⧽ Template:LCM]
The {{LCM}} mathematical function template returns the least common multiple (LCM) of two nonzero integers as a positive integer. An error message is returned when any parameter is not a nonzero integer (currently returns 0 if one parameter is 0 while the other is nonzero, the default value of each parameter being 1) or when the LCM calculation is too complex (this implementation of {{LCM}} uses the {{GCD}} mathematical function template, which currently returns 0 when its limit of ten iterations of the Euclidean algorithm is exceeded, causing a division by zero error in {{LCM}}).
Contents
Usage
- {{LCM|a nonzero integer|a nonzero integer}}
or
- {{lcm|a nonzero integer|a nonzero integer}}
Valid input
Two nonzero integers as parameters.
Examples
Examples with valid input (returns LCM, unless the iterations limit of the Euclidean algorithm is exceeded in the GCD calculation)
Code Result Comment {{LCM|1}} 1 {{LCM|6}} 6 {{LCM|16|6}} 48 {{LCM|16|32}} 32 {{LCM|25|625}} 625 {{LCM|544|119}} 3808 {{LCM|119|544}} 3808 {{LCM|-544|119}} 3808 {{LCM|544|-119}} 3808 {{LCM|-544|-119}} 3808 {{LCM|2089|3571}} 7459819 {{LCM|3571|2089}} 7459819 {{LCM|20891|35713}} Expression error: Unexpected < operator. {{LCM|308911|355717}} 109884894187 {{LCM|6534273|3557172}} Expression error: Unexpected < operator. {{LCM|{{Fibonacci|12}}|{{Fibonacci|11}}}} = {{LCM|144|89}} 12816 {{LCM|{{Fibonacci|13}}|{{Fibonacci|12}}}} = {{LCM|233|144}} Expression error: Unexpected < operator. {{LCM|{{Fibonacci|14}}|{{Fibonacci|13}}}} = {{LCM|377|233}} Expression error: Unexpected < operator. {{LCM|{{Fibonacci|15}}|{{Fibonacci|14}}}} = {{LCM|610|377}} Expression error: Unexpected < operator. {{LCM|{{Fibonacci|16}}|{{Fibonacci|15}}}} = {{LCM|987|610}} Expression error: Unexpected < operator. {{LCM|{{Fibonacci|17}}|{{Fibonacci|16}}}} = {{LCM|1597|987}} Expression error: Unexpected < operator. {{LCM|{{Fibonacci|18}}|{{Fibonacci|17}}}} = {{LCM|2584|1597}} Expression error: Unexpected < operator. {{LCM|{{Fibonacci|19}}|{{Fibonacci|18}}}} = {{LCM|4181|2584}} Expression error: Unexpected < operator. {{LCM|{{Fibonacci|20}}|{{Fibonacci|19}}}} = {{LCM|6765|4181}} Expression error: Unexpected < operator. {{LCM|20891|35713}} Expression error: Unexpected < operator. {{LCM|{{expr|2*3*5*7*11*13*17*19}}|{{expr|7*17*101*113}}}} 110702561970 {{LCM|{{expr|5^2*7*13*17}}|{{expr|5*7*17*23}}}} 889525 {{mpf|{{LCM|{{expr|5^2*7*13*17}}|{{expr|5*7*17*23}}}}}} Prime factors (with multiplicity) error: Argument must be a nonzero integer
Examples with special input (degenerate cases) giving special output
Code Result Comment {{LCM}} 1 LCM of empty product (1) {{LCM|0}} 0 {{LCM|0|6}} 0 {{LCM|6|0}} 0
Examples with invalid input (returns an error message)
Code Result Comment {{LCM|ten|fifteen}} Expression error: Unrecognized word "ten". {{LCM|6.74|9}} Expression error: Unexpected < operator. {{LCM|2/3|4/9}} Expression error: Unexpected < operator. {{LCM|0|0}} Division by zero.
Code
Version with reduced nesting levels (those are limited by MediaWiki!):
{{#expr: ( abs ( {{{1|1}}} ) ) / {{GCD| ( {{{1|1}}} ) | ( {{{2|1}}} ) }} * ( abs ( {{{2|1}}} ) ) }}
Previous version:
{{ifint| ( {{{1|empty}}} )
| {{ifint| ( {{{2|empty}}} )
| {{#ifexpr: ( {{{1}}} ) * ( {{{2}}} ) = 0
| {{error| LCM error: Integers must be nonzero }}
| {{expr| ( abs ( {{{1}}} ) ) / {{GCD| ( {{{1}}} ) | ( {{{2}}} ) }} * ( abs ( {{{2}}} ) ) }}
}}
| {{error| LCM error: Arguments must be nonzero integers }}
}}
| {{error| LCM error: Arguments must be nonzero integers }}
}}
