Find Least Common Multiple of 12, 15 and 75 by listing out the factors.

LCM( 12, 15, 75 ) = 300

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, . . .

The multipliers of 15 are: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300, 315, . . .

The multipliers of 75 are: 75, 150, 225, 300, 375, . . .

We can see that:

LCM( 12, 15, 75 ) = 300

This solution can be visualized using a Venn diagram.

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