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I don't know how to do this question, I don't even know where to begin, I absolutely don't get it. If I could have a hint or a brief understanding on how to do this it would really help

Charles chooses several consecutive positive integers, he wrote down some of the numbers in red and the others in blue. Is it possible that the sum of the lcm of the blue numbers and the lcm of the red numbers is a power of 2?

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    hint to start: Let $C$ denote the set of numbers Charles chooses, that is, $C = \{n,n+1,\ldots,n+k \}$. Then $B$ and $R$ form a partition of $C$, that is $B \cap R = \varnothing$ and $B \cup R = C$. Can we say something about the lcm of all the numbers in $B$ and $R$? – 2017-01-09

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