The lowest common multiple of 5 positive integers is 194040. Find the minimum possible sum of these 5 numbers?

Question

If 1^3 + 2^3 + 3^3 = m^2 where m is also an integer.
What are the next three consecutive positive integers such that the sum of their individual cubes is equal to a perfect square?

Answer 1

194040 has factors of 2,2,2,5 and 4951 all of which are prime numbers and their sum is 4970