My colleague Julia is preparing a talk about factoring for an elementary audience, and she created the following problem to use as a warm-up:
Take a two‑digit number ab, and find the least common multiple of a, b, and ab. For example, if you take the number 35, then LCM(3, 5, 35) = 105. For which two‑digit number ab is LCM(a, b, ab) the greatest? (The notation ab is used to indicate the two‑digit number with tens digit a and units digit b, which is equal to 10a + b. This notation is used to distinguish the two‑digit number ab from the product ab.)
Here are some math jokes about factors:
What do you call an amount that exactly divides a recipe for a sweet confection?
A fudge factor.
What do algebra equations and British television have in common?
An X Factor.
Sadly, both of those are my original jokes. Sorry. To cleanse your palate, check out one of Randall Munroe’s original jokes about factoring: