Encyclopedia > Least common multiple

  Article Content

Least common multiple

The least common multiple (LCM) of two integers a and b is the smallest positive integer that is a multiple of both a and b. If there is no such positive integer, i.e., if either a or b is zero, then lcm(a,b) is defined to be zero.

The least common multiple is useful when adding or subtracting fractions, because it yields the lowest common denominator. Consider for instance

2/21 + 1/6 = 4/42 + 7/42 = 11/42
the denominator 42 was used because lcm(21,6) = 42.

In case not both a and b are zero, the least common multiple can be computed by using the greatest common divisor (or GCD) of a and b,

a b
lcm(a, b) = ---------
gcd(a, b)
 
Thus, the Euclidean algorithm for the GCD also gives us a fast algorithm for the LCM. As an example, the LCM of 12 and 15 is 12 × 15 / 3 = 60.



All Wikipedia text is available under the terms of the GNU Free Documentation License

 
  Search Encyclopedia

Search over one million articles, find something about almost anything!
 
 
  
  Featured Article
Canadian Charter of Rights and Freedoms

... a charter of rights in the constitution was a much debated issue. Prime Minister Pierre Trudeau very much wanted it, but many of the provincial leaders did not. Trudea ...

 
 
 
This page was created in 44.8 ms