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Number theory Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

Carl wrote a list of 10 distinct positive integers on a board. Each integer in the list, apart from the first, is a multiple of the previous integer. The last of the 10 integers is between 600 and 1000. What is this last integer?

(A) $640$ (B) $729$ (C) $768$ (D) $840$ (E) $990$

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