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16 x 15 x 12 = 2,880

 

2,880 / 12   = 240

 

240 = (1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 40, 48, 60, 80, 120, 240) >>Total = 20

 

240 is the smallest positive integer.

15 = 3 * 5

12 = 2 * 2 * 3

16 = 2 * 2 * 2 * 2

 

^{Take each prime factor the greatest number of times it occurs  (in red)}

^{2 * 2 * 2 * 2 * 3 * 5 = 240 = LCM}