L.C.M. (Least Common Multiple)
We take an example of Multiplication :
Example : Multiple of 12
Result : 12, 24, 36, 48, 60, 72, 84, 96,108, 120, 132, 144, 156, 168, 180, 192,........., n
Example : Multiple of 15
Result : 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 220,................, n
As per above examples we can say that least common number in 12 & 15 is "60", So 60 is the LCM of 12 & 15.
LCM Definition : Least Common Number which is exactly divisible by given number, It is called LCM.
There are 2 methods in L.C.M.
1) Factorization Method
2) Division Method
1) Factorization Method:
If we want to find the LCM of 2 or more than 2 numbers at that time we have to calculate prime factor of each number and take common factors (if common factors are in at least 2 number then we have to take that number as common factor) only 1 time and take other remaining numbers, multiply Common Factor and remaining number.
Example : Find the LCM of 12 & 15
Solution : 12 = 2*2*3*
15 = 3*5
So, LCM = 3*2*2*5 = 60 ,
NOTE: Here, We are taking 3 only one time because 3 is common in both.
2) Division Method:
If we want to find the LCM of 2 or more than 2 numbers at that time we have to divide all given number as per given below and multiply the Quotients.
Example : Find the LCM of 12 & 15
Solution :
2| 12 15
2| 6 15
3| 3 15
5| 1 5
| 1
LCM = 2*2*3*5 = 60
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Questions:
1) Find LCM of 18, 24 & 36 with the help of Factorization Method.
Ans: 72
Prime Factor of 18 = 2 * 3 * 3
24 = 2 * 2 * 2*3
36 = 2 * 2 * 3*3
LCM = 2 * 2 * 3 * 3 * 2 = 72
2) Find the LCM of 36, 84, 132, 180 with the help of Factorization Method.
Ans: 13860
Prime Factor of 36 = 2*2*3*3
84 = 2*2*3*7
132 = 2*2*3*11
180 = 2*2*3*3*5
LCM = 2*2*3*3*5*7*11 = 13860
3) Find the LCM of 18, 36 & 84 with the help of Division Method.
Ans: 6
2| 18 36 84
2| 9 18 42
3| 9 9 21
3| 3 3 7
7| 1 1 7
| 1
LCM = 2*2*3*3*7 = 252
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