Here is the problem: I have less than 500 plant pots. I wish to set them out neatly on my bench. When I try setting them out in 2's there is 1 left over, I then try 3 in each row & again there's 1 left over. This repeats when I try 4's, 5's & 6's with 1 over each time. I then try setting them out with 7 in each row and get none left over. How many pots did I have? First try solving this mathematically, then check your answer with this program. (I wrote this program as a fun way to double check my answer. The way I solved it mathematically is not the same way the program runs, though you could have done it this way. The program just goes through all the oppositions and checks them. This is a bit tedious by hand but since the program runs so fast it is not an issue. (Hint: First try to find the least common multiple of 2, 3, 4, 5, & 6 and work from there. If you are good at arithmetic and know your factors this won't take you long. Or you can use a little number theory and the prime factorization of each number to figure out the LCM. Or there is always the brute force method.)
