Math CentralQuandaries & Queries


Question from devin, a student:

Subject: lcm of polynomials

x^3-8 , x^3-4, x^2+4x+4

Hi Devin,

You solve this problem very much as you would find the lcm of integers. First you factor into "prime" factors (factor completely) and then build the lcm from these factors.

Here is an example. Find the lcm of 6, 7 and 4.

First the prime factors

6 = 2 times 3
7 = 7
4 = 22

The lcm is then built from these primes, 2, 3 and 7. Look at each at the prime decomposition and select the highest power of each of the primes.

The highest power of 7 is 1.
The highest power of 3 is 1.
The highest power of 2 is 2.

Thus the lcm is 7times 3 times 22 = 84.

Now try the same procedure with your polynomials.


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