Question 1103370: the multiples of 12 and of 21 are written in order. What is the smallest positive difference between a multiple of 12 and a multiple of 21?
Found 2 solutions by Alan3354, math_helper:
Answer by Alan3354(69443)   (Show Source):
Answer by math_helper(2461)  (Show Source):
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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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