What is the minimum sum of two natural numbers whose lowest common multiple is 729?

We can see that 729 is 9 times 81, meaning that $$729=9^3=3^6$$

We want to find the minimum sum of the two numbers, in order to get the minimum sum, we would want the numbers to be as close to each other a possible, which would be when both are equal to $$3^3=27$$, giving the sum to be 54

But in that case, 729 would not be the lowest common multiple; it would be 27 itself. 

We see that since the 729 is a prime number multiplied repeatedly, the only number that can have LCM as 729 are 1 and 729 itself. 

Therefore, the minimum sum would be 730. 

Hence, Option E is the correct answer.