The LCM of two numbers x and y is the least number among all the common multiples of x and y.
Example:
Find the LCM of 6 and 9.
Solution:
Multiples of 6 are 6,12,18,24,30,36,…
Multiples of 9 are 9,18,27,36,…
So the common multiples are 18, 36, …
So, LCM of 6 and 9 is 18.
Since this is difficult always to write all the multiples especially in case of large numbers, there is a procedure to find LCM.
Finding LCM:
There are two methods to find LCM.
a) Division method:
The process of finding LCM using common division method is shown through the following example.
Example: Find the LCM of 12 and 45.
Solution:
LCM = 3 x 4 x 15 = 180.
b) Factorization method:
The process of finding LCM using common division method is shown through the following example.
Example: Find the LCM of 12 and 45.
Step-1: Find the prime factorization of the given numbers.
12 =22 x 3
45 = 32 x 5
Step-2: Take the product of highest powers of all the prime numbers involved in the factorizations (from the step 1).
The prime numbers involved in these factorizations are 2,3 and 5 and their highest powers are 22, 32 and 5.
So, LCM of 12 and 45 = 22 x 32 x 5 = 180.
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