Highest Common Factor

1. Dec 21, 2009

Gringo123

I've been stuydying how to work out the highest common factor and lowest common multiple of 2 numbers. I had no problems until I had to work these things out for 3 different numbers. The numbers are 18, 24 & 27.
I was able to work out that 216 is the LCM, but I cannot see how I can work out that 3 is the HCF. Can anyone explain this to me?

2. Dec 21, 2009

Fightfish

Wrong board, but I'll answer anyway (this thread will be moved right, mods?)
The technique to use is prime factorisation; factorise each of the numbers into a product of prime numbers eg. 24 = 2^3 * 3. Due to the unique properties of prime numbers, you can obtain both the LCM and HCF by simply comparing the prime factor representations of the numbers involved.

3. Dec 26, 2009

icystrike

It will be simple (=
18=2x3²
24=2³x3
27=3³

LCM simply means take the maximum degree among the all the primes.
&
HCF simply means take the minimum degree among the all the primes.

For instance LCM of 18 , 24 and 27 , we will take 2³x3³ for we see 2 to the power of 3 is the maximum degree which is taken from 24 and 3 to the power of 3 is the maximum degree as taken from 27.

HCF is the otherwise, we take the minimum degree of prime.
HCF(18,24,27)=$$2^{0}\times3^{1}$$=3

Btw, Fightfish this thread is belong under what category?

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