LCM & HCF.....

Hello learners,

Let's start this blog with the hope that you have attempted all the questions given in the previous blog and also without any query......

In this blog I am sharing about a very basic topic and may be everyone is very well aware about this but the reason of sharing about  these terms and concepts is to refreshing the previous knowledge....

So yeah, the topic of this blog is mentioned above  i.e., LCM and HCF ......

Let's first write it's full form and define the terms with an example and process...

1. LCM ( least common multiple )

It is the product of the greatest power of each prime factor, involved in the numbers.

For clarification let's take an example

LCM of 6 and 20 is 2² × 3¹ × 5¹ which is equal to 60 .

LCM(6,20) = 2² × 3¹ × 5¹

                   = 60

Let me show you how to calculate this👇🏼....  

         

Now let's define Other term ,

1. HCF ( highest common factor )

It is the product of the smallest power of each common prime factor in the numbers.

Example: 

HCF of 6 and 20 is 2, which can be written as

HCF( 6,20 ) = 2¹

                   = 2

Let's see how to calculate it systematically👇🏼...

And the relation between LCM & HCF is

HCF( a,b ) × LCM ( a,b ) = a × b

And

LCM( p,q,r ) = p×q×r× HCF( p,q,r )

                                    ____________________________

                             HCF(p,q)× HCF(q,r)× HCF(p,r)

 And

HCF( p,q,r ) = p×q×r× LCM( p,q,r )

                                    ____________________________

                           LCM(p,q)× LCM(q,r)× LCM(p,r)

Now let me give you some questions to check your understanding :

Q.  Find the LCM and HCF of the following:

  

   1.  12 , 15 & 21

   2.  17 , 23 & 29

 

   3.  8 , 9 & 25

So with the hope that you will attend these questions I am ending this blog.......

And if you face any difficulty comment below 👇🏼....