What is LCM and HCF and How to Solve LCM and HCF Questions?

In this post, we will discuss the concept of LCM and HCF and solve few questions on LCM and HCF by using simple division and multiplication method for IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC CGL, SSC CHSL and other competitive exams.

LCM and HCF - What is LCM and HCF and How to Solve LCM and HCF Questions?

In  IBPS PO, IBPS Clerk, SBI PO, SBI Clerk, SSC CGL, SSC CHSL and other competitive exams, there are always questions asked on LCM and HCF. LCM and HCF is the most basic concept and one can find LCM and HCF of a given pair of numbers by using simple division and multiplication method. Scoring marks in LCM and HCF is super easy if one has a thorough knowledge of the concept.In this post, we will discuss what is LCM and HCF and also solve few frequently asked questions by using simple division and multiplication method. This post is divided into three parts- the first part is the Introduction of few terms and their definitions which are important while solving LCM and HCF questions, the second and the third part will discuss Module 1 and Module 2 from the concept of LCM and HCF. This will help you solve LCM and HCF questions using simple division and multiplication method.

What do mean by Factors?

A factor of a number are all those numbers, which exactly divide the given number. “Exactly divides” means that when a number is divided by its factor the reminder is always  0.
Example: 1,2,and 4 are the factors of 4.
Likewise the factors of 5, 6, 7, 8 are given below.
LCM and HCF

What do you mean by Multiples?

Multiples of a number are those numbers which are exactly divisible by the given number.
Example: The multiples of 4 are 4,8,12,16,20 etc.
Like wise the multiples of the number 5, 6, 7, 8 are given below.
LCM and HCF
Prime and Composite Numbers

A Prime Number is a number which has only two factors.
The first factor is “1” and the second factor is the number itself.

Example: As you can look in the table given below, the numbers in the table have only two factors.

LCM and HCF

A Composite Number is a number which has more than two factors.

Example: As you can look in the table given below, the numbers in the table have more than two factors.
LCM and HCF

The difference between a prime number and a composite number is that- a prime number has exactly 2 factors and a composite number has more than two factors. 

What is LCM and HCF?

LCM: Least Common Multiple
LCM of two given numbers is the least number which is exactly divisible by each one of the given number.

Example 1:
Question: Find the LCM of 3 and 4.
Solution:
Step 1:
Given below is the list of multiples that 3 and 4 have.
LCM and HCF

The least common multiple between the two numbers is 12.
Therefore, The LCM of 3 and 4 is 12.

Example 2: 
Question: Find the LCM of 12.36,45,60.
Solution: 
It is not possible to write down the multiples of all the numbers as it is a long procedure. So, we follow a method to solve such questions.
Step 1:

Eliminate the numbers which are the factors of other numbers.

Step 2:

LCM and HCF

Step 3:
2 x 2 x 3 x 5 = 180
Therefore, 180 is the smallest number which is divisible by all the numbers.

LCM and HCF

HCF: Highest Common Factor

HCF of two or more given numbers is the highest number which exactly divides all the numbers.

Example 1:
Question: What is the HCF of 12 and 16?
Solution: Write down all the factors of the given number and check which is the highest common factor between the two given number-
LCM and HCF

Therefore, the HCF of 12 and 16 is 4.

It is a tedious job to write all the factors first and then finding the highest common factor. So we take the simple division method which will help us to find the HCF of the given number. In this method, the divisor which gives the remainder as zero becomes the HCF of the given number.
If the numbers given are prime numbers then there HCF is 1.

LCM and HCF

Therefore, the HCF of 12 and 16 is 4.

Example 2:
Question: What is the HCF 10,35 and 50?
Solution:
At a given point of time, we can find HCF for only numbers.
In this case, for example, lets take the 3 numbers as a, b, c.
We first find the HCF of a and b.
Suppose the HCF of a and b is ‘d’.
Then we take the HCF of d and c and then their HCF becomes the HCF of a,b and c.
Step 1:

HCF of 10 and 35

LCM and HCF

Step 2:
The HCF of 10 and 35 is 5.
Now we take the HCF of 5 and 50.

LCM and HCF

Therefore the HCF of 10,35 and 50 is 5.

How to find LCM and HCF of a Fraction or Non-Integer Numbers?
LCM of a Fraction or Non – Integer Numbers

LCM and HCF

Take the LCM of all the numerators and the HCF of all the denominators to find the LCM of given pair of non-integer numbers


Example: 
Question: Find the LCM of 2/3 and 4/6.
Solution: 

 

Step 1:
LCM of 2 and 4 is 4.
Step 2:
HCF of 3 and 6 is 3.
Therefore, LCM of 2/3 and 4/6 is 4/3.
HCF of a Fraction or Non-Integer Numbers
LCM and HCF

Take the HCF of all the numerators and the LCM of all the denominators to find the HCF of given pair of non-integer numbers.

Example:
Question: Find the HCF of 10/20 and 5/2.
Solution:
Step 1: 
HCF of 10 and 5 is 5
Step 2: 
LCM of 20 and 2 is 20
Therefore, HCF of 10/20 and 5/2 is 5/20 i.e. 1/4

Model 1: Questions on LCM and HCF

Question 1:What will be the smallest number divisible by 6,8,18,24,and 36.
Solution:
Step 1:
6,8 and 18 are eliminated because they are the factors of 24 and 36.

Step 2:

LCM and HCF

Step 3:

2 x 2 x 2 x 3 x 3 = 72.
Therefore, 72 is the number which is exactly divisible by 6,8,18,24,and 36.

Question 2: Which is the largest number that can exactly divide 52,65 and 143.
Solution:

Step: HCF of 52 and 65

LCM and HCF

Step 2: HCF of 13 and 143

LCM and HCF

Therefore, The largest number that can exactly divide 52, 65 and 143 is 13.

Model 2:  What is the product of LCM and HCF

For any two positive numbers a and b

LCM and HCF

L = LCM of a and b

H = HCF of a and b
In the examination any three digits will be given and we need to find the one missing number.
Example: What is the product of LCM and HCF?
Question: The LCM and HCF of two positive numbers are 300 and 30 respectively. If one number is divided by 4, the quotient is 15, then what is the other number?
Solution:
Step 1:
LCM = 300
HCF = 30
As a is divided by 4 and the quotient is 15,
a/4 = 15
a = 15 x 4
a = 60; b =?
Step 2:
a x b = L x H
60 x b = 300 x 30
b = 300×30/60

b = 150Therefore, the other number is 150.

Do write down in the comment section how this blog helped you to solve LCM and HCF Questions.

Stay tuned for our next post.

LCM and HCF
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Sukhwinder
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Sukhwinder

Very helpful

Sanjay
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Sanjay

Nicely explain

Varun
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Varun

Solved my confusion entirely, worth recommending and easy explanation helped me understand thoroughly, Thank you

Dr. Sanjay Sen
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Dr. Sanjay Sen

Incomplete , requires further advanced discussions , also some corrections needed.

RAJ
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RAJ

Super. But need More number of problems.

Rishabh Tayal
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Rishabh Tayal

worth it!

Google user
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Google user

Really very helpful for me to clear my basics of math……. For this kind of information provided… Really thankful of u sir……..

Sudhanshu
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Sudhanshu

Guys, I Love your blogs …..They are very simple and fast to understand.

Suchismita Nayak
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Suchismita Nayak

Very helpful…… Bt require more discussion about it

Phani
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Phani

Very helpful

Shyam
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Shyam

Good

avi
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avi

how to find lcm &
hcf of quadratic eq type question like x^2+4x+2 and 2x^2+4x-5

Ropesh
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Ropesh

Really Helpful! Learnt these during our X class however later I forgot. However, This blog helped me a lot to recall how LCM & HCF are calculated

Anne
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Anne

This was really helpful… Thanks

Prem kumar
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Prem kumar

Dai poda

Arvind
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Arvind

Nice

Arvind
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Arvind

Very helpful

Yogesh dwivedi
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Yogesh dwivedi

Thanks

Sandeep kumar
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Sandeep kumar

Very nice

Prasad
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Prasad

Quite useful and simple to understand

lalita
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lalita

thank you for telling very simple method to solve HCF and LCM

Sheuli sasmal
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Sheuli sasmal

Helpful

Nikhil
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Nikhil

Very Very usefull

SNEHAL
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SNEHAL

I think its cool way to solve these types of numerical. Thanks for your help, hope further new and simple tricks will help all students.

Manpreet singh
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Manpreet singh

1/2 , 3/5 , 4/7 , 5/7
LCM ???

some guy
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some guy

The hard way we used to do it compared to this… i feel scammed. SO helpful… thank you

shiju
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shiju

Thank you

fexon mtima
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fexon mtima

Very helpful. Thank you.

indradev yadav
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indradev yadav

NICE SOLUTION

indradev yadav
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indradev yadav

Very good explanation and clearify
http://.pgk.pxxstory.com

Mohit
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Mohit

Thank you..very nice..

Sanjay
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Sanjay

h – दो संख्याओं का म स 21 और ल स 4146 तो पहली संख्या 100 और 300 के बीच में अंक है तो संख्याएं ज्ञात कीजिये ।

biggay
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biggay

very nice

Aishwarya Thakur
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Aishwarya Thakur

Somebody please help me with the second example under LCM.

How is 2×2×3×5 = 180 ????

Rajkumar
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Rajkumar

to the point, very nice.

Jegyansha Rao
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Jegyansha Rao

Perfect explanation with understandable words and examples👏

Akshay Dinde
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Akshay Dinde

Beautifully explained

Sophia Mathew
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Sophia Mathew

Well explained! Thank You so much!

Grishma
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Grishma

easily understanding and so helpful

uuusshudhj
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uuusshudhj

very useful

IRFAN YOUSF
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IRFAN YOUSF

Thanks

Pravin Garje
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Pravin Garje

Very helpful…..thank u so much.

Manoj kumar
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Manoj kumar

Very good

shekhar
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shekhar

LCM example step 3 , you missed to multiply by 3 to get 180

Ganesh
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Ganesh

Y some numbers eliminated not understand

Ganesh
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Ganesh

Why some numbers eliminated not understand

Ch Tirupati rao
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Ch Tirupati rao

We are know the LCM
More explanation about HCF

Sujata
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Sujata

Very helpful. Thank you.

Suresh Kumar
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Suresh Kumar

Very nice

Ramesh
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Ramesh

I like the way of explaing