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What Is HCF And LCM ?

In science, the outright kind of LCM is the most un-normal number, while the outright sort of HCF is the most eminent normal part. hcf indicates the best factor that exists between something like two given numbers, while L.C.M. The trait of the most modest number can be totally unique in relation to something like two numbers. hcf is likewise called the most eminent normal variable (GCF) and the LCM is additionally called the lowest shared factor.

Test quick on HCF and LCM

To find the HCF and LCM, we have two significant procedures which are the amazing factorization technique and the division methodology. We have learned the two strategies in our past classes. Both H.C.F. Moreover, LCM is a division system. Allow us to figure out the connection among HCF and LCM with the assistance of condition here. Also, we will handle a portion of the issues to more readily figure out these two thoughts. This article is incredibly important for the comprehension of fundamental and helper segments like Class 4, Class 5, Class 6, Class 7 and Class 8.Click here

Hcf And Lcm Definition

We realise that the components of a number are ideal divisors of that specific number. How would we continue on toward the most prominent normal component (H.C.F.) and least normal component (L.C.M.).33 inches in feet

Hcf Definition

As indicated by the laws of arithmetic, the best normal divisor or gcd of no less than two positive numbers is the biggest positive number that separates the numbers without leaving the rest of. For instance, take 8 and 12. HCF 8 and 12 will be 4 considering the way that all that number that can partition both 8 and 12 is 4.

Lcm Definition

In science, the LCM or LCM of two numbers, for instance, an and b, is tended to as lcm(a, b). Moreover, LCM is the littlest or littlest positive number that can be separated from both an and b. For instance, let us take two positive entire numbers 4 and 6.

The results of 4 are: 4,8,12,16,20,24…

The results of 6 are: 6,12,18,24… .

The normal results of 4 and 6 are 12, 24, 36, 48… and so on. The littlest normal number of that package would be 12. Presently let us attempt to follow the LCM of 24 and 15.

LCM of 24 and 15.

LCM of 24 and 15 = 2 × 2 × 2 × 3 × 5 = 120

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Lcm Of Two Numbers

There might be two numbers, 8 and 12, whose LCM we need to find. Allow us to build the results of these two numbers.

8 = 16, 24, 32, 40, 48, 56,…

12 = 24, 36, 48, 60, 72, 84,…

As might be self-evident, the most surprising or least normal part of two numbers, 8 and 12, is 24.

Hcf And Lcm Conditions

The recipe that contains both HCF and LCM:

Consequence of two numbers = (HCF of two numbers) x (LCM of two numbers)

Let An and B be two numbers, then, at that point, as per the condition;

A x B = H.C.F. (a, b) x lcm (a, b)

We can likewise develop the above condition as for HCF and LCM:

hcf aftereffect of two numbers = consequence of two numbers/L.C.M of two numbers


L.C.M of two numbers = Aftereffect of two numbers/H.C.F. of two numbers

How To Follow Hcf And Lcm?

We can utilize the joined techniques to follow the HCF and LCM of the given numbers.

Prime Factorization Procedure

division procedure

Permit us to independently become familiar with the two techniques.

HCF by Prime Factorization Method

Take an instance of following the most remarkable normal component of 144, 104 and 160.

Allow us now to make the standout components 144, 104 and 160.

144 = 2 × 2 × 2 × 2 × 3 × 3

104 = 2 × 2 × 2 × 13

160 = 2 × 2 × 2 × 2 × 2 × 5

The normal components of 144, 104 and 160 are 2 × 2 × 2 = 8. huh

From that point, HCF(144, 104, 160) = 8

In this way, we can see here that 16 is the best number that isolates 160 and 144.

In this manner, HCF(144, 160) = 16

Lcm By Prime Factorization Technique

To track down the LCM of two numbers 60 and 45. One technique to track down the LCM of the given numbers, by substitute strategies, is given underneath:

First investigate the incredible components of each number.

60 = 2 × 2 x 3 × 5

45 = 3 × 3 × 5

Then, increase every component by the times it works out.

Assuming a similar variable happens no less than a few times in two given numbers, copy the component when it happens.

Event of numbers in the above model:

The thing in this issue is impossible, considering the way that HCF given in this issue is more unmistakable than LCM which is silly.

Hcf And Lcm Equation

The LCM and HCF equation of two numbers ‘a’ and ‘b’ is communicated as HCF (a, b) × LCM (a, b) = a × b. As such, the recipe of HCF and LCM expresses that the result of any two numbers is equivalent to the result of their HCF and LCM. To find out about the LCM and HCF relationship, visit this page which portrays the connection among HCF and LCM.

Hcf And Lcm Stunts

On the off chance that 1 is the HCF of 2 numbers, their LCM will be their item. For instance, the HCF of 2 and 3 is 1, presently the LCM of 2 and 3 will be 2 × 3 = 6.

For two coprime numbers, the HCF is generally 1. For instance, let us take two co-indivisible numbers 4 and 5, we can see that their HCF is 1 since co-indivisible numbers have no normal variable other than 1.

Distinction Among Hcf And Lcm

The distinction between the idea of HCF and LCM is given in the accompanying table:


The full type of HCF is Most noteworthy Normal Component.

The full type of LCM is Least Normal Different.

HCF is the biggest of the multitude of normal elements of the given numbers

LCM is the littlest of the relative multitude of normal products of the given numbers.

HCF of given numbers can’t be more noteworthy than any of them.

LCM of given numbers can’t be more modest than any of them.

HCF and LCM Examples

Example 1: Find the HCF and LCM of 14 and 28 using prime factorization.


HCF of 14 and 28:

The prime factors of 14 = 2 × 7

The prime factors of 28 = 2 × 2 × 7

The HCF is the product of the common prime factors of the given numbers. The common prime factors of 14 and 28 are 2 and 7.

Therefore, the HCF of 14 and 28 is 2 × 7 = 14.

LCM of 14 and 28:

The prime factors of 14 = 2 × 7 = 21 × 71

The prime factors of 28 = 22 × 71

Now, we will find the product of only those factors with the highest powers. This will be 22 × 71 = 4 × 7 = 28


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