# Math Help - stupid question about

hi,
what is the more "mathematical or scientific method to find LCM and HCF?

instead of just thinking? I remember short division could do the job, but forget how to do so

Hope someone explain me together with the concepts. Thanks!!!

2. Originally Posted by louis1234
hi,
what is the more "mathematical or scientific method to find LCM and HCF?

instead of just thinking? I remember short division could do the job, but forget how to do so

Hope someone explain me together with the concepts. Thanks!!!
Hi louis1234,

Not a stupid question at all. Look here for LCM and here for HCF.

3. Originally Posted by masters
Hi louis1234,

Not a stupid question at all. Look here for LCM and here for HCF.

thanks

but what i want to know is, how to use short division to do that.

Maybe below will explain. Like this, find the L.C.M. of 2,5 and 6
how to further to it if 5 is not divisible by 2

2 | 2 5 6
------------

4. Originally Posted by louis12345
thanks

but what i want to know is, how to use short division to do that.

Maybe below will explain. Like this, find the L.C.M. of 2,5 and 6
how to further to it if 5 is not divisible by 2

2 | 2 5 6
------------
The simplest method to find LCM is to factor each number into the product of primes:

$2 = 2^1$
$5 = 5^1$
$6 = 3^1 * 2^1$

Multiply all the different factors with the largest exponents. Since the different factors are 2, 5, and 3 and exponents are all 1, we simply multiply:

LCM = $2 * 5 * 3 = 30$

I'm not sure how short division plays into this, though.

A better example might be: Find the LCM of 8, 12, and 15.

Factor each number into the product of primes:

$8=2^3$
$12=2^2*3$
$15=3^1*5^1$

The different factors are 2, 3, and 5. Now multiply all the different factors using their largest exponents:

LCM = $2^3*3^1*5^1=120$