Monday, March 4, 2013

Everyday LCMs

Here's an exercise that I'm planning to use in my remedial arithmetic class in the near future. The question is: For each of the following number ranges, state (i) the LCM (least common multiple), (ii) some everyday examples that use that LCM, and (iii) an explanation of why that number is convenient.

(a) {1, 2, 3}.
LCM is 6. Examples: Six-pack of soda, beer, donuts, etc. Convenient because you can divide them evenly whether you have one, two, or three people.

(b) {1, 2, 3, 4}.
LCM is 12 (a dozen). Examples: 12-pack of beer, dozen eggs, hours on a clock, etc. Convenient because you can divide them evenly among either one, two, three, or four people (or dishes or periods).

(c) {1, 2, 3, 4, 5}.
LCM is 60. (And see next exercise.)

(d) {1, 2, 3, 4, 5, 6}
LCM is also 60. Examples: 60 seconds in a minute, 60 minutes in an hour, 360 degrees in a circle (6×60), etc. Convenient because you can divide them evenly into one, two, three, four, five, or six periods, as desired. (See also: Babylonian numerals.)