Question 1103370

If looking strictly for positive differences, the answer would be 3 (zero is not positive nor negative).  

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12, 24, 36, 48, 60, 72, 84,  …

21, 42, 63, 84, …


The smallest positive difference can not be smaller than 3 because 12=2*2*3 and 21=3*7  so you see 3 is a common factor.  Thus, any positive differences between 12k and 21m  (k=1,2,3,…; m=1,2,3,…)  must be evenly divisible by 3.   

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