## Archive for September 24, 2010

### Confounding Factors

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 ofa,b, andab.For example, if you take the number 35, then LCM(3, 5, 35) = 105. For which two‑digit numberabis LCM(a,b,ab) the greatest? (The notationabis used to indicate the two‑digit number with tens digitaand units digitb, which is equal to 10a+b. This notation is used to distinguish the two‑digit numberabfrom the productab.)

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: