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

The multipliers of 8 are: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, 112, 120, 128, . . .

The multipliers of 24 are: 24, 48, 72, 96, 120, 144, . . .

The multipliers of 15 are: 15, 30, 45, 60, 75, 90, 105, 120, 135, . . .

The multipliers of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, . . .

We can see that:

LCM( 8, 24, 15, 5 ) = 120