What is the sum of all positive integers r that satisfy
lcm [ r, 700 ] = 7000
Your question doesn't make sense!
If you were thinking of the LCM[10,700], it doesn't equal 7,000, but 700!.
What is the sum of all positive integers r that satisfy
lcm [ r, 700 ] = 7000
factorization
\(\begin{array}{|rcll|} \hline lcm [ r, 2^2\times 5^2\times 7^1] &=& 2^3\times 5^3 \times 7^1 \\\\ r &=& 2^3\times 5^3 \times 7^0 & = 1000 \\ r &=& 2^3\times 5^3 \times 7^1 & = 7000 \\ sum &=& & =8000 \\ \hline \end{array}\)
The sum of all positive integers r is 8000