Finding Least Common Multiple (LCM) by FactoringDate: 10/19/2001 at 01:13:45 From: Laura Subject: Prime factoring My math book has the example: Find the least common multiple of 6, 8, and 9. 6 = 2 x 3 8 = 2 cubed 9 = 3 squared the least common multiple of 6, 8, and 9 is 2 cubed x 3 squared, or 72. I understand that 8 x 9 = 72, but what happened to the 6 or 2 x 3? I just don't get how to "figure prime factors and find the product of the greatest power of each prime factor." Please help. Laura Date: 10/19/2001 at 19:08:35 From: Doctor Terrel Subject: Re: Prime factoring Hi Laura, Yes, LCM is often a tricky thing to understand, especially going at it via prime factorizations first. Remember what LCM stands for in the beginning... M = multiple C = common L = least (or lowest) MULTIPLES: 9 ==> 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, ... 8 ==> 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, ... 6 ==> 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, ... COMMON: Try to find a number or number(s) that appear in ALL 3 LINES. In the above sample, we only find 72. There are other larger ones, but it takes too long to write them. To do that in a fun way, go to The M.O.M. Game: http://www.geocities.com/ttrotter3/mom.html LEAST [smallest, first, etc.] That has to be 72, this time. Now via PRIME FACTORIZATION: For 6 it is 2 x 3; for 8 it is 2 x 2 x 2; and for 9 it is 3 x 3. The task now before you is to make a collection or set - as small as possible - of those primes in which you can find all the factors of any given number. LCM (6, 8, 9) = {2, 3, ...} [6 is there so far] = {2, 3, 2, 2, ... } [two more 2's were needed for 8] = {2, 3, 2, 2, 3} [another 3 was needed for the 9] 2 x 3 x 2 x 2 x 3 = 72. So LCM(6, 8, 9) = 72. I hope this helps. - Doctor Terrel, The Math Forum http://mathforum.org/dr.math/ |
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