# CLASS-8LOWEST 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.)