Problem #1267

 1267 Two farmers agree that pigs are worth $300 and that goats are worth$210. When one farmer owes the other money, he pays the debt in pigs or goats, with "change" received in the form of goats or pigs as necessary. (For example, a \$390 debt could be paid with two pigs, with one goat received in change.) What is the amount of the smallest positive debt that can be resolved in this way? $\mathrm{(A)}\ 5\qquad\mathrm{(B)}\ 10\qquad\mathrm{(C)}\ 30\qquad\mathrm{(D)}\ 90\qquad\mathrm{(E)}\ 210$ This problem is copyrighted by the American Mathematics Competitions.
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