# CLASS-4LEAST COMMON MULTIPLE (LCM)

LEAST COMMON MULTIPLE (LCM)

Any number can be a multiple of two or more numbers. Suppose there are two numbers these are 2 and 4.

To find any number of common multiple of the given numbers we should have to find the first common multiple and then multiply it 1 time, 2 times, 3 times.

Product of 2 & 4 is = 2 X 4 = 8.

Thus, the common multiples of 2 & 4 are – 8 x 1 = 8

8 x 2 = 16

8 x 3 = 24

8 x 4 = 32

8 x 5 = 40, …………

So, 8 is the LCM of 2 & 4.

Write the 5 common multiple of the following numbers

Example.1) 3 & 7

Ans.)  Product of 3 & 7 is = 3 X 7 = 21

5 common multiplies of the following multiplies are =   21 x 1 = 21

21 x 2 = 42

21 x 3 = 63

21 x 4 = 84

21 x 5 = 105

So, LCM of the number 3 & 7 is 21 and first five multiples are 21, 42, 63 , 84, 105.

Example.2) 5 & 6

Ans.)  Product of 5 & 6 is = 5 X 6 = 30

5 common multiples of the following multiplies are =  30 x 1 = 30

30 x 2 = 60

30 x 3 = 90

30 x 4 = 120

30 x 5 = 150.

So, LCM of the number 5 & 6 is 30 and the first five multiples are 30, 60, 30, 120, 150.

DIVISIBILITY -

Now we will learn, how to understand which ‘Dividend’ is divisible by which ‘ Divisor’.

Suppose there is a number, that is 453 and we have to find which number will be ‘Divisor’,

Firstly add all the digit of 453 like = 4 + 5 + 3 = 12 , 12 is divisible by 3

BASIC FACTORIZATION -

Basic Factorization is nothing but a simplified multiplication form.

For an example, basic factorization of 24 = 1 x 2 x 2 x 2 x 3.

basic factorization of 36 = 1 x 2 x 2 x 3 x 3.

a) 1 has only one factor and that is the number(1) itself. It is called ‘Unique‘ number.

b) 2, 3, 5, 7, 11, 13 have only two factors, 1 and the number itself, these numbers are called ‘ Prime’ Numbers.

c) Numbers having three or more factor like 4, 6, 8, 10, 12, ……… are called ‘CompositeNumber.

LCM BY BASIC FACTORIZATION THROUGH DIVISION METHOD –

Example.1) Find the Basic Factors of the number 50  - Step.1)  First, consider 50 as dividend and consider the lowest number which is 2 which is count as ‘Divisor’. 50 ÷ 2 = 25. So, 25 is a ‘Quotient’.

Step.2)  Put 25 below the position of 50 and then try to divide. We can find 5 is the lowest ‘Divisor’ for dividing the ‘Dividend25 and we can get 5 as ‘Quotient’.

Step.3) Put 5 below the position of 25 and then try to divide. We can find 5 is the lowest ‘Divisor’ for dividing the ‘Dividend5 and we can get 1 as ‘Quotient’.

So, basic factorization of 50 is  2 x 5 x 5 x 1     (Ans.)

Example.2) Find the Basic Factors of the number 80 - Step.1)  First, consider 80 as dividend and we can find the lowest number which is 2 and 2 will be considered as ‘Divisor’. 80 ÷ 2 = 40. So, 40 is a ‘Quotient’.

Step.2)  Put 40 below the position of 80 and then try to divide. We can find 2 is the lowest ‘Divisor’ for dividing the ‘Dividend40 and we can get 20 as ‘Quotient’ .

Step.3) Put 20 below the position of 40 and then try to divide. We can find 2 is the lowest ‘Divisor’ for dividing the ‘Dividend20 and we can get 10 as ‘Quotient

Step.4) Put 10 below the position of 20 and then try to divide. We can find 2 is the lowest ‘Divisor’ for dividing the ‘Dividend10 and we can get 5 as ‘Quotient

Step.5) Put 5 below the position of 10 and then try to divide. We can find 5 is the lowest ‘Divisor’ for dividing the ‘Dividend5 and we can get 1 as ‘Quotient’.

So, basic factorization of 80 is 2 x 2 x 2 x 2 x 5 x 1    (Ans.)

Example.3) Find the Basic Factors of the number 45 & 30 - Step.1)  First, consider 45 & 30 together as ‘Dividend’ and we can find the lowest number which is 5, and 5 is the common ‘Divisor’ of both the number 45 & 30. If 5 is ‘Divisor’ then, 45 ÷ 5 = 9 is ‘Quotient’ & 30 ÷ 5 = 6 is ‘Quotient’.

Step.2) Now put 9 & 6 below the number 45 & 30 respectively. Consider 9 & 6 as ‘Dividend’ and find the lowest common ‘Divisor’ for both the number 9 & 6. We can find, 3 is the lowest common ‘Divisor’ for dividing both the ‘Dividend9 & 6, we can get 9 ÷ 3 = 3 & 6 ÷ 3 = 2, 3 & 2 as ‘Quotient

Step.3) Now put 3 & 2 below the number 9 & 6 respectively. Consider 3 & 2 as ‘Dividend’ and find the lowest common ‘Divisor’ for both the number 3 & 2. We can find, 1 is the only lowest common ‘Divisor’ for dividing both the ‘Dividend’ 9 & 6 we can get 3 ÷ 1 = 3 & 2 ÷ 1 = 2, 3 & 2 as ‘Quotient

So, LCM by basic factorization of 45 & 30 is 5 x 3 x 1 x 3 x 2 = 90.

(Ans.)

Example.4) Find the Basic Factors of the number 24 & 36  - Step.1)  First, consider 24 & 36 together as ‘Dividend’ and we can find the lowest number which is 2, and 2 is common ‘Divisor’ of both the number 24 & 36. If 2 is ‘Divisor’ then, 24 ÷ 2 = 12 is ‘Quotient’ & 36 ÷ 2 = 18 is ‘Quotient’.

Step.2) Now put 12 & 18 below the number 24 & 36 respectively. Consider 12 & 18 as ‘Dividend’ and find the lowest common ‘Divisor’ for both the number 12 & 18.

We can find, 2 is the lowest common ‘Divisor’ for dividing both the ‘Dividend12 & 18. we can get  12 ÷ 2 = 6 & 18 ÷ 2 = 9, so respectively 6 & 9 is ‘Quotient

Step.3) Now put 6 & 9 below the number 12 & 18 respectively. Consider 6 & 9 as ‘Dividend’ and find the lowest common ‘Divisor’ for both the numbers 6 & 9. We can find, 3 is the only lowest common ‘Divisor’ for dividing both the ‘Dividend6 & 9. we can get 6 ÷ 3 = 2 & 9 ÷ 3 = 3.  so respectively 2 & 3 is ‘Quotient

Step.4) Now put 2 & 3 below the number 6 & 9 respectively. Consider 2 & 3 as ‘Dividend’ and find the lowest common ‘Divisor’ for both the number 2 & 3. We can find, 1 is the only lowest common ‘Divisor’ for dividing both the ‘Dividend2 & 3. we can get 2 ÷ 1 = 2 & 3 ÷ 1 = 3. so, respectively 2 & 3 is ‘Quotient

So, LCM by basic factorization of 24 & 36 is  2 x 2 x 3 x 1 x 2 x 3 = 72              (Ans.)

LCM by basic factorization -

Example.1) Find LCM of 15 & 25. So,  15 = 3 x  5  x  1

25 = 5 x  5  x  1

In the above condition for both, the number of common factor is 5 & 1.

Now to find out the LCM of 15 & 25 multiply common factor 5 ,1 and uncommon factors 3 & 5.

So, product of the factors are = 3 x 5 x 5 x 1 = 75.

75 is the LCM of the 15 & 25.            (Ans.)

There are some other way of solution of about Lowest Common Multiple (LCM) is given below for your more better understanding -

(i) Common Multiple Method Or Listing Method,

(ii) Common Division Method,

(iii) Prime Factorization Method,