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LCM or LCD

Lowest Common Denominator (LCD or LCM ) : The LCD of two numbers is the smallest number which is a multiple of each of the numbers.
In other words, the LCD of two or more numbers is the smallest number which is divisible by all the given numbers.



Example : LCD of 8 and 12

Multiples of 8 : 8,16,24,32,40,48,…

Multiples of 12 : 12,24,36,48,60,…

Common Multiples are : 24,48,…

So LCD = 24 ( smallest of the above)

There are two methods to find the LCD of given numbers:

1) Prime factorization method.

2) Common division method.

Example : Find the LCD of 40 , 36 and 126 by Prime factorization method .


2 : 3 occurrences
3 : 2 occurrence
5 : one occurrence
7 : one occurrence
So LCD = 2 x 2 x 2 x 3 x 3 x 5 x 7 = 2520

Common Division Method : Find the LCD of 84,90 and 120


LCD by ladder method

Example : Finding the LCD of 24 and 36 by Ladder Method.


Steps :

1) Write the given numbers and make a “L" below it.

2) Find the smallest number divisible by both, in this case it is ‘2’.

3) 24/2 = 12 and 36/2 =18, write these numbers below the respective numbers.

4) 12 and 18 both are divisible by 6 so you can directly take 6.

5) So, we get 2 and 3. Now 2 and 3 has only 1 common number.

6) 2/1 = 2 and 3/1 = 3.

7) Then make a ladder given in the example.

8) Multiply all these numbers to get LCD.
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Practice

Find the LCD of the following using prime factorization method:
1) 12,15,20
2) 8,12 and 15
3) 18,24 and 8
4) 32,42
5) 36,48 and 96

Factors and Multiples

Prime and Composite Numbers
Divisibility rules
Prime Factorization
H.C.F or G.C.F
LCM
Application on LCD

From LCM to Factors and Multiples

Number System

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