Suppose a integer α(α > 0) and another integer β (β > 0) are given. When we add α one or more times and get β we call β is a multiple of α.

For example, we add 2 one times get 2, we add 2 twice get 4, we add 2 three times get 6. Therefore, 2, 4, 6, ... are multiple of 2.

We can think of a multiple common for two numbers. Suppose 10 and 15 are given. Multiples of 10 are, 10, 20, 30, 40, 50, 60, ..., while multiples of 15 are, 15, 30, 45, 60, ..., then a multiple common for 10 and 15 are, 30, 60, ...

The least number of the common multiplies, we call it the least common multiple(LCM). For 10 and 15, 30 is the LCM.

Here is a calculator for LCM

For GCD(greatest common divisor), please see Greatest Common Divisor.