Editing Least common multiple (section)

{{Short description|Smallest positive number divisible by two integers}}
[[File:Symmetrical_5-set_Venn_diagram_LCM_2_3_4_5_7.svg|thumb|250px|A [[Venn diagram]] showing the least common multiples of all subsets of {2, 3, 4, 5, 7}.]]

In [[arithmetic]] and [[number theory]], the '''least common multiple''', '''lowest common multiple''', or '''smallest common multiple''' of two [[integer]]s ''a'' and ''b'', usually denoted by {{nowrap|lcm(''a'',&nbsp;''b'')}}, is the smallest positive integer that is [[divisible]] by both ''a'' and ''b''.<ref name=":1">{{Cite web|last=Weisstein|first=Eric W.|title=Least Common Multiple|url=https://mathworld.wolfram.com/LeastCommonMultiple.html|access-date=2020-08-30|website=mathworld.wolfram.com|language=en}}</ref><ref>Hardy & Wright, § 5.1, p. 48</ref>  Since [[Division by zero|division of integers by zero]] is undefined, this definition has meaning only if ''a'' and ''b'' are both different from zero.<ref name="auto">{{harvtxt|Long|1972|p=39}}</ref>  However, some authors define lcm(''a'', 0) as 0 for all ''a'', since 0 is the only common multiple of ''a'' and 0.

The least common multiple of the denominators of two [[Fraction (mathematics)|fractions]] is the "[[lowest common denominator]]" (lcd), and can be used for adding, subtracting or comparing the fractions.

The least common multiple of more than two integers ''a'', ''b'', ''c'', . . . , usually denoted by {{nowrap|lcm(''a'',&nbsp;''b'',&nbsp;''c'', . . .)}}, is defined as the smallest positive integer that is divisible by each of ''a'', ''b'', ''c'', . . .<ref name=":1" />