Common Multiple
Definition

In general, a common multiple is a non-zero multiple that two or more terms have in common.


Example 1: 36x5 is a common multiple of 12x2 and 18x5.


Example 2: 3600x20y5z2 is a common multiple of 12x2y3z and 18x5y.


Example 3: 24x4y3z is NOT a common multiple of 12x2y3z and 18x5y. [Although 24x4y3z is a multiple of 12x2y3z , it is not a multiple of 18x5y.]


Example 4: 6x2 is NOT a common multiple of 12x2y3z and 18x5y. [6x2 is not a factor of either of the terms.]


Definition (Natural Numbers)

In terms of numbers, a common multiple is a non-zero multiple that two or more natural numbers have in common.


Example 1: 36 is a common multiple of 12 and 18.


Example 2: 360 is a common multiple of 12 and 18.


Example 3: 24 is NOT a common multiple of 12 or 20. [Although 24 is a multiple of 12 {(2)(12) = 24}, it is not a multiple of 20 (24 ÷ 20 = 1.2).]


Example 4: 27 is NOT a common multiple of 12 or 18. [27 is not a multiple of either 12 or 18.]


Demonstration (Natural Numbers)
Image only

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