Editing Least common multiple (section)

== Applications ==
When adding, subtracting, or comparing [[simple fraction]]s, the least common multiple of the denominators (often called the [[lowest common denominator]]) is used, because each of the fractions can be expressed as a fraction with this denominator. For example,

:<math>{2\over21}+{1\over6}={4\over42}+{7\over42}={11\over42}</math>

where the denominator 42 was used, because it is the least common multiple of 21 and 6.

=== Gears problem ===
Suppose there are two [[Gear|meshing gears]] in a [[machine]], having ''m'' and ''n'' teeth, respectively, and the gears are marked by a line segment drawn from the center of the first gear to the center of the second gear. When the gears begin rotating, the number of rotations the first gear must complete to realign the line segment can be calculated by using <math>\operatorname{lcm}(m, n)</math>. The first gear must complete <math>\operatorname{lcm}(m, n)\over m</math> rotations for the realignment. By that time, the second gear will have made <math>\operatorname{lcm}(m, n)\over n</math> rotations.

=== Planetary alignment ===
{{See also|Syzygy (astronomy)}}
Suppose there are three planets revolving around a star which take ''l'', ''m'' and ''n'' units of time, respectively, to complete their orbits. Assume that ''l'', ''m'' and ''n'' are integers. Assuming the planets started moving around the star after an initial linear alignment, all the planets attain a linear alignment again after <math>\operatorname{lcm}(l, m, n)</math> units of time. At this time, the first, second and third planet will have completed <math>\operatorname{lcm}(l, m, n)\over l</math>, <math>\operatorname{lcm}(l, m, n)\over m</math> and <math>\operatorname{lcm}(l, m, n)\over n</math> orbits, respectively, around the star.<ref>{{Cite web|url=https://spacemath.gsfc.nasa.gov/weekly/6Page41.pdf|title=nasa spacemath}}</ref>