Find the sum of all positive integers $r$ that satisfy $\text{lcm}[r,700] = 700.$
All positive integers r and their sum are as follows:
1 , 2 , 4 , 5 , 7 , 10 , 14 , 20 , 25 , 28 , 35 , 50 , 70 , 100 , 140 , 175 , 350 , 700>>Total number=18> Total Sum= 1736
+170 Such integers are simply the factors of \(700\). Note that \(700=2^2\cdot5^2\cdot7\), so the sum of its factors is \((1+2+4)(1+5+25)(1+7)=1736\).
