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# What is the sum of all positive integers v for which lcm(v,20)=60.

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What is the sum of all positive integers v for which lcm(v,20)=60.

Jun 28, 2018

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What is the sum of all positive integers v for which lcm(v,20)=60.

$$\begin{array}{|r|r|r|r|c|} \hline v & \text{factor } v &\text{factor } 20 & \text{factor } 60 &\text{lcm}(v,20 ) \\ \hline 3 & {\color{red}3} & {\color{blue}2^2} \times {\color{green}5} & {\color{blue}2^2} \times {\color{red}3} \times {\color{green}5} & 60 \\ \hline 6 & {\color{red}3} \times 2 & {\color{blue}2^2} \times {\color{green}5} & {\color{blue}2^2} \times {\color{red}3} \times {\color{green}5} & 60 \\ \hline 15 & {\color{red}3} \times {\color{green}5} & {\color{blue}2^2} \times {\color{green}5} & {\color{blue}2^2} \times {\color{red}3} \times {\color{green}5} & 60 \\ \hline 30 & {\color{red}3} \times 2\times {\color{green}5} & {\color{blue}2^2} \times {\color{green}5} & {\color{blue}2^2} \times {\color{red}3} \times {\color{green}5} & 60 \\ \hline 12 & {\color{red}3} \times {\color{blue}2^2} & {\color{blue}2^2} \times {\color{green}5} & {\color{blue}2^2} \times {\color{red}3} \times {\color{green}5} & 60 \\ \hline 60 & {\color{red}3} \times {\color{blue}2^2} \times {\color{green}5} & {\color{blue}2^2} \times {\color{green}5} & {\color{blue}2^2} \times {\color{red}3} \times {\color{green}5} & 60 \\ \hline \text{sum } = 126 \\ \hline \end{array}$$

Jun 28, 2018