find LCM of 108, 135 and 162 by long division method.
Please do it fast
Answers
L.C.M. by Long Division Method:
A least common multiple of two numbers is the smallest positive number that is a multiple of both.
Multiple of 3 — 3, 6, 9, 12, 15, 18,…………..
Multiple of 4 — 4, 8, 12, 16, 20, 24,………….
So the LCM of 3 and 4 is 12, which is the lowest common multiple of 3 and 4.
An example of LCM
The LCM of 10, 20,25 is 100. It means that 100 is the lowest common multiple of these three numbers, but there is a question in our mind that can the LCM be (-100)? Since (-100) is lower than 100 and divisible by each of 10, 20, 25, or can it be zero or what will be the LCM of (-10) and 20? Will it be (-20) or (-200)?
For all these questions, there is only one answer that the LCM is only defined for positive numbers and LCM is not defined for 0.
PROCESS OF FINDING LCM
We will do prime factorization in first step of all the numbers.
Then we calculate the number of times each prime occurs in prime factorization and write each number as power of primes.
Then in last step we write all the primes involved and raise each of the primes to highest power present.
Example based on above
Example 1:LCM of 10, 20, 25?
Step 1: 10= 2 × 5
20 = 2 × 2 × 5
25= 5 × 5
Step 2: 10= 21 × 51
20 = 22 × 51
25= 52
Step 3:Primes involved are 2 and 5
Now we raise each of the primes to highest power present i.e.22 × 52 =100. So 100 is required LCM.
Answer:
The LCM of 108, 135 and 162 is 1620.
Step-by-step explanation:
- LCM, least common multiple is the smallest multiple of the given numbers.
- In division method, divide the given numbers by common prime number until the remainder is a prime number or one.
- Find the product of all the divisors and remaining prime numbers, that gives the LCM.
Given the numbers 108, 135 and 162
In the above, the end numbers 2, 5 and 3 are prime numbers.
So, stopping the division there, multiply all the divisors and the remaining prime numbers.
Therefore, the LCM of 108, 135 and 162 is 1620.