# LCM and HCF Concept & Rules for Competitive Exams

LCM and HCF is a very important chapter for all competitive exams. Take any question paper of any competitive exam where Arithmetic is enlisted as a part of Syllabus and see that every competitive examination asked few questions from this chapter. So, we should give the same effort as we give in other Arithmetic chapters like Time and Works, Mixture and Allegation, Ratio and Proportion etc. Here we will discuss the LCM and H.C.F chapter for the shortcut math tricks. Remember that L.C.M and H.C.F also help you to solve other math problem in the tricky method. In this point of view, this chapter is very important for Arithmetic as well as competitive examination.

## Basic Concept and full form of L.C.M and H.C.F

Now, we are going to discuss the basic concept of this tutorial, we should know  HCF stands for Highest Common Factor. And L.C.M is the Least Common Multiple of entire numbers.
What is the LCM of 16 and 24?
A)24 B)48 C)60
16= 2x2x2x2
24=2x2x2x3
Here, common numbers are 2x2x2 and uncommon is 2x3. So the lowest common product is 2x2x2x2x3= 48
So the answer is B. The 48 is the lowest common product of 16 and 24.
What is H.C.F?  H.C.F is the highest common factor of two or more numbers which can divide by all numbers without any reminder. See the example for a better understanding.
What is the HCF of 16 and 24?
A)8 B)48 C)16
16= 2x2x2x2
24=2x2x2x3
Here common numbers are 2x2x2 and uncommon is 2x3. So the HCF is 2x2x2=8
So the answer is option A. The 8 is the common divisor of 16 and 24 without any remainder.
I hope you got the clear concept of this math topic.

## shortcut formula and solved Question

Trick 1:
L.C.M*H.C.F= Multiplication of two numbers.
Trick 2: When the highest number is divided A, B and C and every time become remainder X, then the Highest number will be

Tricks 3: Which is the highest number while dividing by A, B and C, and getting the same remainder every time?
Every time will the same remainder when you divide A, B, and C by
Trick 4: When you dividing A, B and C by a number and getting the reminder x, y and z respectively. Find out by which number are you dividing?
Solved aptitude by math tricks
Aptitude 1: The L.C.M of two numbers is 520 and the HCF 4. If the first one is 52, then the second one will - A) 40 B) 42 C) 50 D) 52
Solution:
We know that L.C.M*H.C.F= Multiplication of two numbers.
Here the first number is 52. Let be the second number is x
Therefore 52 x =4 * 520

So the answer is 40.
Aptitude 2:
Every time will be the same reminder while you dividing 650, 775 and 1250. now find out the number?
A) 15 B) 25 C) 20 D) 30
Solution:
We know- Every time will be the same remainder when we divide A, B and C by:-
HCF of (A-B) and (B-C)
(1250-775), (775-650)
175, 125.
The H.C.F of 175 and 125 is 25. So the answer is option B.