Problem of the Week #19: Monday May 15th, 2023 This is a problem I've posted before, and I've worded it to be a bit less technical. I figured it fits well with this month's theme. As before, these problems are the results of me following my curiosity, and I make no promises regarding the topics, difficulty, solvability of these problems. Please register for an account if you would like to join the discussion below or share your own problems.
a). Consider all pairs of natural numbers that add to 9, which pair has the largest possible Least Common Multiple?
b). Consider all pairs of natural numbers that add to 10, which pair has the largest possible Least Common Multiple?
c). Consider all pairs of natural numbers that add to n, where n is a natural number, which pair has the largest possible Least Common Multiple?
d). Consider all sets of natural numbers that add to 10, which set has the largest possible Least Common Multiple?
e). Consider all sets of natural numbers that add to n, where n is a natural number, which pair has the largest possible Least Common Multiple?
f). Share your own problem inspired by this one.
g). Give one of these questions to a friend/colleague/student/family member to start a mathematical discussion.