LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

LEAST COMMON MULTIPLE (LCM)

__LEAST COMMON MULTIPLE (L.C.M) __

**The L.C.M of two or more natural
numbers is the smallest of the common multiple of the given numbers. For an
example, if we consider 3, 5 & 15 then the common multiples are –**

**Multiples of 3 are – 3, 6, 9, 12, 15, 18, 21, 24, 27,………………….....**

**Multiples of 5 are – 5, 10, 15,
20, 25, 30, 35, 40, 45,……………...…**

**Multiples of 15 are – 15, 30, 45,
60, 75, 90, 105,………………… **

**From the above factors, we can find that,
the Least Common Factors (L.C.M) of the three given number 3, 5, & 15 is 15. (Ans.)**

__METHOD OF FINDING THE L.C.M THROUGH PRIME FACTORIZATION PROCESS
-__

**1) Find the L.C.M of 32 & 48**

**So, 32 = 2 x 2 x 2 x
2 x 2 x 1**

** 48 = 2 x 2 x 2
x 2 x 3 x 1**

**From the above
factorization 2 appears in 32 five times and in 48, 2 appears four
times. And also 3 appears once in a factorization of 48**

**Thus, 2appears
maximum five times and 3 appears maximum one times**

**So, the Least common
factor (L.C.M) of the given numbers 32 & 48 are = 2 x 2 x 2 x 2 x 2 x 3 =
96. (Ans.)**

**2) Find the L.C.M of 32, 48, 72**

**So, 32 = 2 x 2
x 2 x 2 x 2 x 1**

** 48 = 2 x 2 x 2 x 2 x 3 x 1**

** 72 = 2 x 2 x 2 x 3 x 3 x 1 **

**From the above
factorization 2 appears in 32 five times, 2 appears in 48 four times and
2 appears three times in 72. And also **

**3 appears one time in
a factorization of 48 and 3 appears two times in 72.**

**Thus, 2 appears
maximum five times and 3 appears maximum two times**

**So, the Least common
factor (L.C.M) of the given numbers 32, 48 and 72 are = 2 x 2 x 2 x 2 x 2
x 3 x 3 = 288 (Ans.)**

__FIND LEAST COMMON FACTORS (L.C.M) THROUGH COMMON DIVISION METHOD
-__

**1) Find the L.C.M of 18, 24, 27,36 & 72**

__ Step.1)__**
Arrange the given numbers in a row in any order you wish**

__Step.2)__**
Select or take any number as a Divisor which divides exactly minimum of two
given numbers in a row and carries forward the rest of the non-divisible numbers
to the next step.**

** Step.3) Repeat the above process
till no two of the given numbers are Divisible by same number other than
1.**

__Step.4)__**
The product of the divisors and the undivided numbers is the required L.C.M of
the given numbers.**