54 Part 1: The World of Numbers
CHECK POINT
Find the greatest common factor of each pair of numbers.
16. 18 a nd 42- 42 and 70
- 144 and 242
19. 630 and 945
20. 286 and 715
Least Common Multiple........................................................................................................
If you attend a baseball game at which every twelfth person admitted to the stadium receives a
free key ring and every twentieth person gets a free t-shirt, where should you be in line if you
want both? You want a spot that’s a multiple of 12, so that you get the key ring, but you want it to
also be a multiple of 20, so you snag a t-shirt. You also don’t want to be too far back in line, so the
smallest number that does both jobs is what you’re after. Many people would look to be #240 in
line because that’s 12 v 20, but you can move, if not to the head of the line, at least farther up.
The least common multiple, or LCM, of two (or more) numbers is the smallest number that is a
multiple of both. If the LCM is a multiple of both numbers, then both numbers divide the LCM,
and both are factors of the LCM.DEFINITION
The least common multiple of two or more numbers is the smallest number that has
each of the numbers as a factor.The least common multiple of 12 and 20 is much smaller than 240. 240 is a multiple of 12 and of- It is a common multiple, but it’s not the least, or smallest, common multiple. If you look at lists
of the multiples of 12 and 20, you’ll see that 60 is the smallest number to show up in both lists.
Multiples of 12: 12, 24, 36, 48, 60, 72 ...
Multiples of 20: 20, 40, 60, 80 ...
You can stake out the 60th spot in line at the game, get a good seat, and go home with the key
ring and the t-shirt.
Making a list of the multiples of each number and looking for the first number to pop up on
both lists is actually a workable method of finding the least common multiple, if the numbers
aren’t too big. For large numbers, however, it could take a very long time and a lot of multiplying.