# Lowest Common Multiples (LCM) : Basics

In this post we will try to understand what is Least Common Multiple (LCM) and how to calculate LCM step by step. This concept is important because its questions are repeatedly asked in competitive exams.

LCM is basically smallest multiple of given set of numbers.
Let us understand this concept with the help certain examples

Example 1:
suppose you have been asked to find LCM of 2 and 3.
It means that the question is asking you the smallest number which gets fully divided by both number 2 and 3.

We know that LCM (2,3) is 6
It means that 6 is the lowest possible number which gets fully divide by both 2 and 3

Example 2:
Find LCM of 42, 49 and 63
When you calculate LCM you will find that LCM (42,49,63) =>882
It means that 882 is the smallest number which get divided by all three numbers given 42, 49, 63

I hope you understand the basic concept of LCM. Before solving any question it is important to understand the concept behind it so that it gets easier to solve difficult question associated with the concept.
Now we will understand how to find LCM of numbers

## How to find LCM/How to calculate LCM

There are basically two different methods to find LCM of given numbers
1. LCM by prime factorization
2. LCM by common division method

We will study each of then through examples. My only suggestion is to select one method and practice it rigorously so that you can solve the problem easily in the examination hall.

### LCM using Prime Factorization Method

In this method we basically calculate prime factors of all the numbers and then note down individual factors with highest power for LCM. Let us understand this method step by step with examples.

#### 01.Find LCM of 42, 49 and 63 using Prime Factorization Method

Step 1:
Do prime factorization of each number given

The prime factors of the given numbers are:
42 => 2 * 3 * 7
49 => 7 * 7
63 => 3 * 3 * 7

Step 2:
Now in order to find LCM, take each factor and raise it to the highest power available

Hence,
LCM => 2 * 9 * 49 => 882
LCM (42, 49, 63) is 882

So, 882 is the lowest number which gets fully divided by 42, 49 and 63

#### (02) Find the LCM of 150, 210 and 375 using Prime Factorization Method

Step 1:
Calculate Prime Factorization of each number

Step 2:
Now in order to find LCM, take each factor and raise it to the highest power available

Hence,
LCM (150, 210, 375) => 5250
So, 5250 is the smallest number which gets fully divisible by 150, 210 and 375

#### (03) Find LCM of 75, 100, 175 using Prime Factorization Method

Step 1:
Calculate Prime Factorization of each number

Step 2:
Now in order to find LCM, take each factor and raise it to the highest power available

Hence LCM (75,100,175) is 2100

LCM Calculation Explanation (English)

LCM Calculation Explanation using Prime Factorization (Hindi)

### LCM using Common Division Method

This is another method for LCM calculation where we find all the possible factors of given numbers in one go. This method is suitable for one who do not want to waste time calculating individual prime factorization of numbers.

Hence if you are preparing for competition exams, this method is good for you as it consumes less time. Let us understand this method with the help of examples

#### (01) Find LCM of number 8, 9, 10 using common division method

Step 1:
find out all the factors using common division table

The Combined Factors of number 8, 9, 10 are ==> 2 * 2 * 2 * 3 * 3 * 5

Step 2:
Calculate the combined factors to get the LCM
LCM (8, 9,10) => 2 * 2 * 2 * 3 * 3 * 5 ==> 360

Hence 360 is the LCM of given numbers

#### (02) Find the LCM of numbers 42,49 and 63 using common division method

Step 1
Find out all the common factors using common division table

The combined factors of 42, 49, 63 => 2 * 3 * 3 * 7 * 7

Step 02
Calculate the combined factors to get the LCM
LCM (42, 49, 63)==> 2 * 3 * 3 * 7 * 7 ==> 882

Hence 882 is the LCM of given set of numbers

#### (03) Find the LCM of numbers 7, 35, 14, 28 using common division method

Step 01:
Find common factors using common division table

The combined factors of 7, 35, 14, 18 are ==> 2 * 2 * 5 * 7

Step 02:
Calculate the combined factors to get the LCM
LCM (7, 35, 14, 18) ==> 2 * 2 * 5 * 7 => 140

Hence 140 is the LCM of given set of numbers

LCM Calculation using Division Method (English Explanation)

LCM Calculation using Division Method (Hindi Explanation)

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