How to Find LCM in 10 Seconds

Before starting our tricks to find the LCM of a number in 10 seconds.
Let us know “What IS LCM” ?

“LCM” stands for least common multiple(A common multiple can be defined as a number that is a multiple of two or more numbers). It can be defined as the method to find out the smallest common multiple between two numbers or more. “LCM” is also called “LCD” which stands for the least common divisor.

Let’s understand the definition in more detail of LCM with the help of an example: –

LCM,(3,4) = 12, as 12 is divisible by both 3 and 4 as 3 and 4 are called divisors of 12.

We can take another example for better clarity of the concept: –

L.C.M of 15 and 20 will be 2 x 2 x 3x 5 = 60, where 60 is the smallest common multiple or we can say that 60 is the LCM or LCD of the numbers 15 and 20.

Now,we can justify our LCM too, let’s consider the multiples of 15 and 20, we get;

15 → 15, 30, 45, 60,…
20 → 20, 40, 60,…,

Here, we can see that the first common multiple for 15 and 20 is 60. This justifies the method of LCM as correct.

Properties  OF LCM

1. The LCM of given numbers cannot be less than the numbers it self. For example: – LCM of (15, 20) cannot be less than 15 and 20 . It can only be above 20.
2. The Product of LCM *HCF is equal to the product of numbers itself (This property is only applicable to two numbers).
   For example : – LCM (15,  20) = 60
   HCF (15, 20) = 5
   LCM*HCF = 60 x 5 = 300
   Product of numbers = 15 x 20 = 300
   Hence, the product of LCM and HCF is equal to the product of numbers.
3. The LCM of a given co-prime number is equal to the product of the numbers which means if the both numbers are prime(whose factor is 1 and the number itself).
   For eg : – LCM of (5,7) = 5 x 7  =  35

As both numbers are co-prime and only occur in 1 and itself.

Read More : Remember Multiplication Tables of Any Number Using Mental Mathematics

How to Find LCM of Two and Three Numbers?

For smaller numbers, you can simply write the multiples of both numbers and can spot the common multiple.
For example: – 6 and 8

6 = 6, 12, 18, 24, 30, 36……
8 = 8, 16, 24, 32, 40……

Here, 24 is the LCM of (6, 8).

We can find our LCM by 3 methods that are: –

1. By listing the multiple
2. By Prime Factorization
3. By Division Method

Read More : METHODS FOR SOLVING QUADRATIC EQUATION

( 1 ). By Listing Multiples

It is the same method used for the Smaller numbers, you can simply write or list down the elements and can find out the common multiple.

For eg : – 8 and 10
8 = 8, 16, 24, 32, 40, 48, 56, 64, 72, 80…..
10 = 10, 20, 30, 40, 50, 60, 70 , 80, 90……

So, here the LCM of (8, 10) is 40.

( 2). By Prime Factorization

Suppose, we have 3 numbers 12, 18, and 24. We have to write the prime factors of each number individually.

12 = 2 X  2 X 3
18 = 2 X 3 X 3
24 = 2 X 2 X 2 X 3

Now, write the prime factors of all numbers together: –
12, 18, 24 = 2X 2 X 3 X 2 X 3X 3 X 2 X 2 X 2 X 3

Form pairs of the prime factors and write the number once: –
= 2 X 2 X 2 X 3 X3
= 72

LCM of (12, 18, 24) is 72.

Read More : How to find HCF in 10 seconds

( 3). By Division Method

1. First, write all the numbers, and separate them by commas.
2. Now, divide the numbers by the smallest prime number.
3. If any of the numbers is not divisible, then write down that number and follow step b.further.
4. We have to keep on dividing the row of numbers by prime numbers until we get the results as 1 in the complete row
5. Now, the LCM of the numbers will be equal to the product of all the prime numbers we obtained in the method

Let us understand the division method with the help of an example: –

1. Find LCM of 8 and 10 by the division method.

Let’s draw a table and find out according to the previous steps:

table inserts

Therefore, LCM of (8, 10) = 2 x 2 x 2 x 5 = 40

So, these are the traditional methods of finding LCM.

Read More: QUADRATIC EQUATIONS

Now, Let’s Learn the Trick to Find out LCM.

To learn this , you have to study a little concept previously: –
GCF = GCF abbreviated for Greatest Common factor. It is the greatest common factor that divides both numbers.

For eg : – 18 = 2 x 3 x 3
24 = 2 x 2x 2x 3

The numbers have one 2 and one 3 in common.
So, GCF  = 2 x 3 = 6

GCF of (18, 24) = 6

Now, let’s come to our topic “LCM TRICKS”

( 1 ). 14 and 20

Step 1 = Find out the GCF (Greatest Common Factor)
GCF (14,20) = 2

Step 2 = Divide the GCF by either of the number (you can choose any of the numbers, so choose which is easier to divide)

Here, we are choosing 14.
14/2 = 7

Step 3 = Take the answer from the previous step and multiply it by another number.
= 7 x 20 = 140

Step 4 = 140 is your answer.

Read More : Sum of cubes of n natural numbers

( 2 ). 18 and 27

Step 1 = Find out the GCF (Greatest Common Factor)
GCF (18,27) = 3 x 3 = 9

Step 2 = Divide the GCF by either of the number (you can choose any of the number, so choose which is easier to divide)
Here, we are choosing 18.
18/9 = 2

Step 3 = Take the answer from the previous step and multiply it by another number.
= 2 x 27 = 54

Step 4 = 54 is your answer.

Read More : Basic Concept Of Angles In Geometry

( 3 ). 20 and 26

Step 1 = Find out the GCF (Greatest Common Factor)
GCF (20,26) = 2

Step 2 = Divide the GCF by either of the number (you can choose any of the numbers, so choose which is easier to divide)
Here, we are choosing 20.
20/2 = 10

Step 3 = Take the answer from the previous step and multiply it by another number.
= 10*26 = 260

Step 4 = 260 is your answer.

Tips = Choose the smaller number to divide as it makes things simpler.

Practice

• 15 and 25
• 30 and 45
• 48 and 60
• 10 and 15
• 21 and 28