# 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

Number System

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