Friday, September 20, 2013

Finding LCM Using Prime Factorization

Like GCF, you can use prime factorization to find the LCM of two or more numbers.  First find the GCF since the LCM and both numbers will share this factor.

Then multiply the GCF to all the remaining prime factors.  You are doing this because the prime factor string for the LCM must account for all the prime factors in your original numbers.  If not then you do not have the LCM.

Notice every prime in the prime factor string for the LCM (2160) is used at least once.  It is important to understand that the prime factor string for the LCM (2160 in this case) is the shortest factor string possible that will account for the prime factor strings of 144 and 1080.  This is the very meaning of least common multiple.  If you multiply the factor sting for 2160 by 2, you have a common multiple of 144 and 1080 but it is not the least common multiple.

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