Preliminaries
Fractions
Multiples of a number are found by multiplying that number by 1, by 2, by 3, by 4, by 5, etc.
Example 1
List the first seven multiples of 9.
9, 18, 27, 36, 45, 54, 63
Common multiples
Common multiples are multiples that are the same for two or more numbers.
Example 2
What are the common multiples of 2 and 3?
The common multiples of 2 and 3 are 6, 12, 18, …
Notice that common multiples may go on indefinitely.
Least common multiple
The least common multiple (LCM) is the smallest multiple that is common to two or more numbers.
Example 3
What is the least common multiple of 2 and 3?
The smallest multiple common to both 2 and 3 is 6.
Example 4
What is the least common multiple of 2, 3, and 4?
The least common multiple of 2, 3, and 4 is 12.
