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.
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?
What do you mean by Multiples?
Like wise the multiples of the number 5, 6, 7, 8 are given below.
A Prime Number is a number which has only two factors.
Example: As you can look in the table given below, the numbers in the table have only two factors.
A Composite Number is a number which has more than two factors.
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?
Question: Find the LCM of 3 and 4.
Given below is the list of multiples that 3 and 4 have.
The least common multiple between the two numbers is 12.
Therefore, The LCM of 3 and 4 is 12.
Question: Find the LCM of 12.36,45,60.
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.
2 x 2 x 3 x 5 = 180
Therefore, 180 is the smallest number which is divisible by all the numbers.
HCF: Highest Common Factor
Question: What is the HCF of 12 and 16?
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.
Therefore, the HCF of 12 and 16 is 4.
Question: What is the HCF 10,35 and 50?
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.
HCF of 10 and 35
The HCF of 10 and 35 is 5.
Now we take the HCF of 5 and 50.
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
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
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.
Question: Find the HCF of 10/20 and 5/2.
HCF of 10 and 5 is 5
LCM of 20 and 2 is 20
Therefore, HCF of 10/20 and 5/2 is 5/20 i.e. 1/4
Question 1:What will be the smallest number divisible by 6,8,18,24,and 36.
Question 2: Which is the largest number that can exactly divide 52,65 and 143.
Step 2: HCF of 13 and 143
Therefore, The largest number that can exactly divide 52, 65 and 143 is 13.
For any two positive numbers a and b
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.
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