GCD

: 136.330 Intro to Algebra: GCD
   By Anonymous on Wednesday, October 30, 2002 - 01:28 am: Edit Post

I'm not sure on how to find the GCD (other that trial and error) when you are given three numbers.
Example:
12.3:find the greatest common divisor adn the least common multiple of the given set of integers
{36,-60,90}


   By Sasho on Wednesday, October 30, 2002 - 02:01 am: Edit Post

Approach 1: First find the GCD of the first two using the Euclidean Algorithm; call it a; and then find the GCD of a and the third number using the same algorithm. Here is the whole story with the numbers you give. (Note that you may ignore "-" since (-a,b) is the same as (a,b)).

90=(1)(60)+30
60=(2)(30)+0

So (90,60)=30.

Next, find (36,30):

36=(1)(30)+6
30=(5)(6)+0

So (36,30)=6. Consequently the GCD of 36, 60 and 90 is 6. So, the same is true for the GCD of 36, -60 and 90

Approach 2. Use the fundamental thereom of arithmetic. Roughly, factor all three numbers as product of primes and use the primes "common" to all three.


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