LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

LOWEST COMMON MULTIPLE (LCM)

**LOWEST COMMON
MULTIPLE (LCM)**

**The lowest
common multiple (LCM) of two or more number is the smallest of the common
multiples of those numbers**

**Example- the
multiples of 3 should be 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36,…….etc.**

**The multiples of 5 should be 5, 10, 15, 20, 25, 30, 35, 40, 45,
50,……etc.**

**The multiples of 6 should be 6, 12, 18, 24, 30, 36, 42, 48, 54,
60,...etc.**

**From the
multiples of the given number, we should find the smallest or the lowest common
multiple of 3, 5, & 6 is 30.**

**Methods of
Finding LCM –**

**You will be pleased to know that, there are only two
methods of finding the LCM of two or more numbers respectively.**

**a) by prime
factorization b) by division**

**To find LCM
by PRIME FACTORIZATION –**

**Step.1) First of all, we have to express each number as a product of prime factors.**

**Step.2) Take
each prime factor the greatest number of times it appears in any of the prime
factorization of the numbers.**

**Step.3) The
product of the prime factors in Step.2 is the LCM of the numbers.**

**Example.- Find the LCM of 125, 150, and 625.**

**Answer) 125 = 5 X 25 = 5 X 5 X 5**

** 150 = 5 X 30 = 5 X 5 X 6**

** 625 = 5 X 125 = 5 X 5 X 25 = 5
X 5 X 5 X 5**

**We can observe from the above, the greatest
number of times that 5 appears as a factor of any of the numbers is two times **

**Then LCM = 5
X 5 = 25**

**To find LCM
by division –**

**Step.1)
Divide the numbers by a prime number which is a factor of at least two of the
given numbers **

**Step.2) write
the quotients and carry forward the numbers which are not divisible.**

**Step.3)
repeat Step.1 & Step.2 till no two of the numbers have common factors.**

**Step.4) Please note, the
product of the divisors of all the steps and the remaining numbers should be the LCM
of the given numbers.**

**Example.-**

**
**

**Find the LCM of 24, 36, 96**

**So, LCM of
24, 36, & 96 is **

**= 2 X 2 X 3 X 2 X 3 X
4 **

**= 288 (Ans.)**