| 释义 |
Least Common MultipleThe least common multiple of two numbers  and  is denoted  or  and can be obtainedby finding the Prime factorization of each
 | (1) |
 | (2) |
 s are all Prime Factors of and , and if does not occur in one factorization, then the corresponding exponent is 0. The least common multiple is then
 | (3) |
 be a common multiple of  and  so that
 | (4) |
 and  , where  and  are Relatively Prime by definition of the GreatestCommon Divisor  . Then  , and from the Division Lemma (given that  isDivisible by and  ), we have  is Divisible by , so
 | (5) |
 | (6) |
 ,
 | (7) |
 | (8) |
 | (9) |
 | (10) |
 | (11) |
 | (12) |
 | (13) |
 | (14) |
 | (15) |
References
Guy, R. K. ``Density of a Sequence with L.C.M. of Each Pair Less than  .'' §E2 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 200-201, 1994.
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