In
arithmetic and
number theory, the
least common multiple (also called the
lowest common multiple or
smallest common multiple) of two
integers a and
b, usually denoted by
LCM(a, b), is the smallest positive integer that is
divisible by both
a and
b. Since division of integers by zero is undefined, this definition has meaning only if
a and
b are both different from zero. However, some authors define lcm(
a,0) as 0 for all
a, which is the result of taking the lcm to be the
least upper bound in the
lattice of divisibility.