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 👇🏼....


           



Comments

Post a Comment

Popular posts from this blog

Properties of numbers 🔢

Image
We know about various types of numbers as discussed in previous blog , if anyone unable to retrieve then go through it once again ..... Now we will learn about various properties of different types of numbers .... First of all let's list down all the properties:- 1. Commutative property 2. Associative property 3. Distributive property 4. Additive identity 5. Multiplicative inverse 6. Closure property 7. Transitive property It is obvious that Everyone will think that what is the benefit of learning these properties of numbers in mathematics so let's understand the importance of properties in mathematics..... Properties form the backbone of mathematical concepts. By learning properties, students gain a deeper understanding of how numbers and operations behave, which lays a solid foundation for tackling more complex mathematical topics. Also, Understanding properties enhances problem-solving abilities by providing strategies for simplifying expressions, identifying patterns, and d...
Read more

Trigonometry basics ∆.....

Image
Hello learners 👋🏼....... Let's start the new blog on the topic i.e. trigonometry which surrounded by the 6 entities written as follows :- 1. Sin A (Sine of angle A) 2. Cos A (Cosine of angle A) 3. Tan A (Tangent of angle A) 4. Cosec A (Cosecant of angle A) 5. Sec A (Secant of angle A) 6. Cot A (Cotangent of angle A) Trigonometry is a vast chapter so in this blog we will take only one topic i.e. trigonometric ratios .... Trigonometric ratios means the relation between the entities and the angle of triangle and the sides of the triangle 📐...... Let's first see the relation between these entities with one another..... Now let's see the relation between the entities and the angle and sides of the right angled triangle.... May be you all know the tricks of learning this trigonometric ratios still let me tell you the trick..... Sin A      Cos A       Tan A Pandit     Badri     Prasad    Har      ...
Read more