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Q. How to find LCM of 72,180,360

Ans : There are three methods to Find LCM -

1. FACTOR TREE METHOD 
2. PRIME FACTORISATION METHOD
3. DIVISION METHOD

1. Factor Tree Method :

72

2*  36

2* 2* 18

2* 2* 2*9

2* 2* 2* 3*3

180

2*90

2*2*45

2*2*3*15

2*2*3*3*3*5

360

2*180

2*2*90

2*2*2*45

2*2*2*3*15

2*2*2*3*3*5

So LCM is least common multiple which is 2*2*2*3*3**5 =360

(Here We write all common factors & rest factors both)

2. Prime Factorisation method :

[ 72 ]=

2 | 72

2 | 36

2 | 18

3 | 9

3 | 3

   | 1

= 2*2*2*3*3

[180]=

2 | 180

2 | 90

3 | 45

3 | 15

5 | 5

   | 1

= 2*2*3*3*5

[360]=

2 | 360

2 | 180

2 | 90

3 | 45

3 | 15

5 | 5

   | 1

= 2*2*2*3*3*5

So LCM = 2*22*3*3*5 = 360

3. Division method of LCM

2 | 72 , 180 , 360

2 | 36 , 90 , 180

2 | 18 , 45 , 90

3 | 9   , 15 , 45

3 | 3   , 5   , 15

5 | 1   , 5   , 5  

   | 1   , 1   , 1

So LCM is = 2*2*2*3*3*5 = 360