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

The multipliers of 32 are: 32, 64, 96, 128, 160, 192, 224, 256, 288, 320, . . .

The multipliers of 48 are: 48, 96, 144, 192, 240, 288, 336, . . .

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

We can see that:

LCM( 32, 48, 72 ) = 288

This solution can be visualized using a Venn diagram.

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