Editing Least common multiple (section)

== Overview ==
A [[Multiple (mathematics)|multiple]] of a number is the [[product (mathematics)|product]] of that number and an integer. For example, 10 is a multiple of 5 because 5 × 2 = 10, so 10 is divisible by 5 and 2. Because 10 is the smallest positive integer that is divisible by both 5 and 2, it is the least common multiple of 5 and 2. By the same principle, 10 is the least common multiple of −5 and −2 as well.

=== Notation ===
The least common multiple of two integers ''a'' and ''b'' is denoted as lcm(''a'', ''b'').<ref name=":1" /> Some older textbooks use [''a'', ''b''].<ref name="auto"/><ref>{{harvtxt|Pettofrezzo|Byrkit|1970|p=56}}</ref>

=== Example ===
:<math>\operatorname{lcm}(4, 6)</math>

Multiples of 4 are:

:<math> 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, ...</math>

Multiples of 6 are:

:<math> 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, ...</math>

''Common multiples'' of 4 and 6 are the numbers that are in both lists:

:<math> 12, 24, 36, 48, 60, 72, ...</math>

In this list, the smallest number is 12. Hence, the ''least common multiple'' is&nbsp;12.