Tuesday, 2 May 2017

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 and SSC CGL Exam.

LCM and HCF


In SBI PO, IBPS PO and SSC CGL 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 thorough knowledge about 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?


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 given number. In this method the divisor which gives the reminder 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 = 300x30/60
b = 150

Therefore, 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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