Write down multiples of each number until you find the first common multiple:

The multipliers of 12 are: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 132, 144, 156, 168, 180, 192, 204, 216, 228, 240, 252, 264, 276, 288, 300, 312, 324, 336, 348, 360, 372, . . .

The multipliers of 60 are: 60, 120, 180, 240, 300, 360, 420, . . .

The multipliers of 72 are: 72, 144, 216, 288, 360, 432, . . .

We can see that:

LCM( 12, 60, 72 ) = 360

This solution can be visualized using a Venn diagram.

The LCM is equal to the product of all the numbers on the diagram.