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Least common multiple
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<p>In <a href="/facts/Arithmetic/hvHwkbMV">arithmetic</a> and <a href="/facts/Number_theory/zhoa7zrc">number theory</a>, the least common multiple, lowest common multiple, or smallest common multiple of two <a href="/facts/Integer/PUwwrawx">integers</a> <i>a</i> and <i>b</i>, usually denoted by lcm(<i>a</i>, <i>b</i>), is the smallest positive integer that is <a href="/facts/Divisible/DKNa2GvC">divisible</a> by both <i>a</i> and <i>b</i>. Since <a href="/facts/Division_by_zero/wXK7t2Ge">division of integers by zero</a> is undefined, this definition has meaning only if <i>a</i> and <i>b</i> are both different from zero. However, some authors define lcm(<i>a</i>, 0) as 0 for all <i>a</i>, since 0 is the only common multiple of <i>a</i> and 0. </p><p>The least common multiple of the denominators of two <a href="/facts/Fraction_(mathematics)/ghnQE9B3">fractions</a> is the "<a href="/facts/Lowest_common_denominator/vdf2gKmo">lowest common denominator</a>" (lcd), and can be used for adding, subtracting or comparing the fractions. </p><p>The least common multiple of more than two integers <i>a</i>, <i>b</i>, <i>c</i>, . . . , usually denoted by lcm(<i>a</i>, <i>b</i>, <i>c</i>, . . .), is defined as the smallest positive integer that is divisible by each of <i>a</i>, <i>b</i>, <i>c</i>, . . . </p>