HCF and LCM Concept Shortcut Trick

Hey Guys, Are you facing difficulty while solving HCF and LCM problems? Don’t worry, just follow the post and  your all difficulties and doubt will be cleared. Here we have mentioned the basic concept of HCF and LCM along with the shortcut tricks to solve all problems.

Learn Aptitude- Free Aptitude Questions and Answer

Why you should learn HCF and LCM?

If you want to be strong in Mathematics and Aptitude, then you have to be strong in HCF and LCM. HCF and LCM are two backbones of Mathematics.  As like you need food to make your body function similarly you have to be strong in LCM and HCF to do solve further mathematics. Because you will use this concept in every step of mathematics like Addition, Substraction, Calculus and other solutions.

What is the concept of Factor?

A bunch of numbers multiplied with each other to form a new number is called factor of that new number.

How to calculate the factor of a number?

Let us understand the concept of factor by taking an example:

Example: Find the factor of 24, 25, 28?

Solution: (i) 24= 2 × 2 × 2 × 3

(ii) 25= 5 × 5

(iii) 28 = 2 × 2 × 7

I think the concept of factor is now cleared.

HCF (Highest Common Factor)

HCF of two or more number is a number which divides each and every number exactly. In genral, we can say that the highest common factors between two or more numbers is called HCF of that number.

Common Factor

Common factor is the factors which are  present in both the number is called common factor.

Example: Factor of 6= 2, 3

& 12= 2, 2, 3

So we can say that 2 and 3  are the common factor of both the number.

Example of HCF of two numbers

Q. Calculate the HCF of 6 and 12

Factor of 6= 2 , 3

Factor of 12= 2, 2, 3

Here Common factors are 2 and 3

So HCF = 2 × 3=6

Q. Find the HCF of 6 and 14?

HCF and LCM concept solution

LCM (Least common multiple)

LCM is a least number which is divisible by all the given numbers. In other words, we can say that LCM is the product of highest factor of a given number.

Example: LCM of 6, 8

6= 2, 3

8= 2, 2, 2

So LCM= 2 × 2 × 2 × 3= 24

Example 2: LCM of 6 and 14?

HCF and LCM of 6, 14

Important Formulas

  • HCF × LCM = Product of numbers

HCF and LCM of Decimal Number

Lets take an example to understand How to find the HCF and LCM of Decimal number. 

Q. Find the GCD and LCM of the number 0.6, 0.18 and 1.2?

Step-1: First of all check what is the number of digits after  ‘.’ (Dot) point.

HCF and LCM of decimal number

Step-2: Convert all the digits after ‘.’ point into two digits. If one digit is present, put ‘0’ to make it two digits.

HCF and LCM of fraction

Step-3: Remove ‘.’ dot from all the number.

               60       18     120

Step-4: Calculate HCF of 60, 18, 120

HCF and LCM of fraction STEP

Step-5: Calculate LCM of 60, 18, 120

HCF and LCM of fraction step-4

So LCM= 2 × 3 × 2 × 5 × 3 × 2=360

Step-6: Divide the calculated result by 100 to calculate HCF and LCM of the given numbers.

HCF= 6/100=0.06

LCM= 360/100= 3.60

HCF and LCM of Fraction

\fn_jvn HCF= \frac{HCF of (Numerator)}{LCM of (Denominator)}

\fn_jvn LCM= \frac{LCM of (Numerator)}{HCF of (Denominator)}

Q. Find the LCM and GCD of  \fn_jvn \frac{6}{21}, \frac{8}{35} and \frac{12}{63} ?

Solution: 

 \fn_jvn LCM= \frac{LCM( 6, 8, 12)}{HCF( 21, 35, 63)}= \frac{24}{7}

\fn_jvn HCF = \frac{HCF(6, 8, 12 )}{LCM(2, 35, 63 )}= \frac{2}{315}

HCF and LCM of Power of a Number

Q. Find the GCM and LCM of 6², 6¹³, 6 ^18, 6^19? (^=Power)

Solution: HCF= 6²

LCM = 6^19

Q. Find the LCM and GCM of 3^-2 , 3^-12, 3^-23, 3 ^-32? (^=Power)

Solution: HCF= 6²

LCM = 6^19

HCF and LCM of Power of Polynomial

Q. What is the LCM and HCF of 2ab, 6a²b, 8a²b² ?

Solution: Given Expression= 2ab, 6a²b, 8a²b²

We can write 2ab, 6a²b, 8a²b²= 2ab, 2 × 3 a²b, 2³a²b²

So our final HCF= 2ab

and LCM= 2³a²b²

Q. What is the LCM and HCF of x² – xy, x – y, 3x – 3y, x²- 2xy + y² ?

Solution: Given Expression= x² – xy, x – y, 3x – 3y, x²- 2xy + y

We can write  as x( x – y), x – y, ( x – y)²

So our final HCF= x – y

and LCM= x ( x-y)² 

I think your concept regarding this topic is cleared. If something is missing in this post, then kindly let me know about that.

Number system Questions with Answers

Number System Questions with Solution: Hey Guys, Do you know, the number system questions are one of the cool problems in the Aptitude section of Mathematics. You just have to add, substract, multiply or divide one number with another number. I think you are very much aquented with the number system problems. So lets discuss  different problems of number system with their solutions.

 

 

Number System Questions

Number System Questions with Solutions

Q.1 What will be the solution of 34598205 × 999=?

(A) 34563606747
(B) 34563606795
(C) 34563606022
(D) 34563444222

Answer: (B) 34563606795

Solution:Here we have two  process to solve this question. First way we can multiply 34598205 with 999 which will be lengthy. So we have to follow the second method i.e:

34598205 × ( 1000 - 1 )

=34598205000 - 34598205

= 34563606795

Q.2 What is the value of 998 × 112 + 998 × 88= ?

(A) 199600
(B) 156666
(C) 456221
(D) 196632

Answer: (A) 199600

Tips: To solve this question we have to use distributive law:

Solution:  998 × 112 + 998 × 88= 998 × ( 112 + 88) =998 × 200 = 199600 

Related Topics:

Q.3 What is the value of 

742 × 742 + 258 × 258 + 2 × 742 × 258= ?

(A) 10000000
(B) 45668222
(C) 1000000
(D) 4522588

Answer: (C) 1000000

Tips: Use ( a + b )²= a² + b² + 2ab

Solution: 742 × 742 + 258 × 258 + 2 × 742 × 258= (742)² + (258)² + 2 × 742 × 258= (742 + 258)²=1000²=1000000

Q.4 Find the value of  $ for which 236$62 is divisible by 3 and must be an odd number?
(A) 3
(B) 5
(C) 7
(D) 9

Answer: (D) 9

Tips: Use the divisible formula for 3 i.e A number is divisible by 3 if the sum of all the digit of the number is divisible by 3.

Solution: Sum of the given number 2 + 3 + 6  + 6 + 2= 18

So possible answer is 2, 

Q.5 Weather 876744 is divisible by 88?
(A) Yes
(B) No

Answer: (A) Yes

Tips: Use divisible formula of 11 and 8.

Solution: 88= 11 × 8

  • Sum of digits at odd place - Sum of digits at even place = ( 8 + 6 + 4) - ( 7 + 7 + 4)= 18 - 18= 0 which is divisible by 11 So 876744 is divisible by 11
  • Last 3 digit of 876744 is 744 which is divisible by 8, so 876744 is divible by 8.

So, 876744 is divisible by 88 because 876744 is divisible by both 11 and 8.

Q.6 What will be the unit digit in the multiplication of (5227)³¹³ ×(91)³²¹?
(A) 1
(B) 3
(C) 7
(D) 9

Answer: (C) 7

Solution: We have to calculate the unit digit in (5227)³¹³ × (91)³²¹

As we know 74 having 1 as unit digit and (5227)³¹³ 's unit digit can be calculated as per the power of 7 and (91)³²¹ unit digit can be calculated by the help of 1.

So we can write (7)³¹³× (1)³²¹=(7)³¹² × 7 × (1)³²¹= ((7)4)78  × 7 × 1

Hence our required unit digit = ( 1 × 7 × 1) = 7

Q.7  What is the minimum number we have to add with 2019 to obtain a number which is completely divisible by 11?

(A) 12
(B) 5
(C) 6
(D) 4

Answer: (B) 5

Tips: Use formula  Required Number = Divisor - Remainder

Solution:

NUMBER SYSTEM QUESTIONS So our Required Number= 11 - 6 = 5

Q.8  What is the minimum number we have to subtract with 2019 to obtain a number that is completely divisible by 11?

(A) 12
(B) 5
(C) 6
(D) 4

Answer: (B) 5

Tips: Use formula  Required Number =Remainder

Solution:

NUMBER SYSTEM QUESTIONS So Our Required Number=6

Q.9 What will be the sum of 1² + 2 ² + 3² + 4² + 5²+ ……..+ 890² ?

(A) 396494
(B) 396495
(C) 396496
(D) 396497

Answer: (B) 705761100

Tips: Use the series formula  1² + 2 ² + 3² + 4² + 5²+ ........+ n²= ½n(n+1) (2n + 1)

Solution: In 1² + 2 ² + 3² + 4² + 5²+ ........+ 890² here n= 890

So as per the formula we have: ½ × 890(890+1) (2×890 + 1) = 445 × 891 × 1780= 705761100

Q.10 What will be the sum of 1³ + 2³ + 3³ + 4³ + 5³+ ……..+18³​ ?

(A) 705761101
(B) 128608721
(C) 128608722
(D) 12860855

Answer: (C) 128608722

Tips: Use the series formula  1³ + 2³ + 3³ + 4³ + 5³+ ........+ n³= ½n²(n+1)²

Solution: In 1³ + 2 ³ + 3³ + 4³ + 5³+ ........+ 18³ here n= 18

So as per the formula we have: ½ × 18²(890+1)²= 162 × 793881= 128608722

100+Problems on Ages- Shortcut Trick, Formula

Do you think the problems on ages are difficult? Not at all!, its very easy. Just use your brain to solve these problems. In all the competative examination you will find atleast 2-3 questions based on ages. Because the examinor wants to test your brain not your knowldge. So its very important to use some tricks and formula to solve these types of question.

Get all the basic trick and concept to solve problems based on Age questions with solutions for competitive examinations like SSC, Railway Bank PO, and all other Government examinations.

Problem-Based-on-Ages

 

Before going into the problems based on age,  we have to clear our concept about Age. After that, you will be able to do each Question easily.

For Quantitative Aptitude Click Here

Concept of age

Do you know? You will get problems on ages in 3- format:

  1. Past Age
  2. Present Age
  3. Future Age

First of all study the following image

Problems on Ages

In the above figure, you can not jump from past to future directly. You have to first move to Present and then future. Similarly, you can’t jump from future to past directly. You have visit past through the present.

Similarly, in a question, if past age is given, then you have to calculate the present age and then future age. If the future age is given, then you have to calculate the present age and then past age.

Q.1 Let us say in my family there are 5 members and the sum of the age of the members is 75. Then what will be the sum of age of our family member after 5 years?

(A) 90

(B) 80

(C) 100

(D) 110

The sum of age of my family member= 75
After 5 years meant the age of each family member will increase by 5
As there are 5 members, so the total increase in age of my family member after 5 years will be= 5×5= 25

∴Sum of age = 75+25=100

Here you have to note that after 5 Years, age of each member will increase simultaneously. You should not add only 5.

Concept of Age difference

Q.2 If the difference of age between me and my brother is 4 years then what will be the age difference between me and my brother after 5 years?

(A) 55

(B) 60

(C) 50

(C) 4

Your answer is (C) 4 Years

Because when my age will increase 5 years, my brother’s age will also increase simultaneously.

Hence, the age difference will remain same.

Note: You have to remember that the age difference between two people will never change.

Q.3 If the age gap of Rahul and his brother is 60 years and after 8 years the sum of their age is 156 years. What is the current age of Rahul’s Grand Mother?

(A) 100

(B) 120

(C) 80

(D) 70

Your answer is (A) 100 Years

As per the question the difference of age i.e 

Grand Mother – Rahul=60

Now again sum of the age after 8 years= 156

Hence, sum of present age i.e 

Grandmother + Rahul= 156 -( 8+8) = 140

So Grand Mother’s age =\frac{140+60}{2}=\frac{200}{2}= 100 Years

Q.4 The age gap between Subham and Rashmita is 16 years. 6 years ago the proportion of their age was 3:5 respectively. What is the current age of Subham?

(A) 40

(B) 24

(C) 30

(D) 46

Your answer is (C) 30 Years

From the question we have the age difference = 16

Six years ago ratio= 3:5

Difference of age ratio= 5x-3x= 2x

2x= 16

⇒x- 8

So age of Subham = 3×8= 24

Hence, present age = 24+6=30

Q.4 The ratio of Rubi and Kabi is 3:7 and  the sum of their age is 90. What is the age of Rubi after 12 years?

(A) 9

(B) 21

(C) 27

(D) 39

Age of Rubi and Kabi= 3:7= 3x:7x

Sum of age =90

So 3x+7x= 90

⇒10x= 90

⇒x= 9

Age of Rubi= 9×3=27

∴After 12 years = 27+12=39

 

Q.4 Joty is 40 years old and Situ is 60 years old. How many years ago was the ratio of their age was 3:5?

(A) 10

(B) 20

(C) 37

(D) 05

Answer: (A)

Solution: \frac{40-x}{60-x}= \frac{3}{5}

⇒x=10

Q.5 The ratio of the present age of Rahul and Sani is 2: 1. The ratio of their age after 30 years will be 7:6. What is the present age of Rahul ?

(A)6 years

(B) 10 years

(C) 12 years

(D) 15 years

 

Answer: (D)

Solution:

So Rahul’s Present age is = 2 ×6= 12 years

Q.6 Jayesh is as younger to Amit as he is older to Prashant. If the sum of the ages of Amit and Prashant is 48 years. What is the age of Jayesh in years?

(A) 22 years

(B) 24 years

(C) 25 years

(D) 28 years

Answer: (B)

Solution: Let the age of Jayesh= x

Let the age of Amit= y

Let the age of Prashant= z

y-x= x-z

2x= y+z= 48

Age of Jayesh (x) = 24 years

Q.7  Nalu is younger to Lipu as he is older to Dipu. If the sum of the ages of 3 friend is 58 years old. What is Nalu’s age?

(A) 29 years

(B) 30 years

(C) 31 years

(D) 32 years

Answer: (A) 29 years