Question

Find the L.C.M of the following numbers 3, 6, 9.

Answer 1

Hint: First, here we should know the difference between highest common factor (HCF) and least common multiple (LCM). After that, we will find LCM of given numbers with the help of the division method. In this method, divide the given numbers by common prime number until the remainder is one. Thus, LCM will be the product obtained by multiplying all divisors.

Complete step-by-step answer:

The Least common multiple (LCM) of two or more than two number is the least number which is exactly divisible by each one of the given numbers whereas highest common factor (HCF) of two or more than two number is the greatest number which is exactly divisible by each one of the given numbers. For example, LCM of 6 and 8 if given as:

So, LCM of 6 and 8 \[=2\times 2\times 2\times 3=24\] .
Here, in the question we are asked to find LCM of three numbers i.e. 3, 6, 9. So, we will solve it by division method.
 

Here, we can see that LCM of 3, 6, 9 \[=2\times 3\times 3=18\].
Thus, we got the required answer as 18.

Note: Another method to solve the problem is by using the prime factorization method i.e. by finding prime factors of every individual number and multiplying that prime number occurred maximum time to get the answer.
Be careful while finding LCM as it has a similar method that of finding HCF. Now if we find HCF of 3, 6, 9 we get
factors of 3 \[=3\times 1\]
factors of 6 \[=3\times 2\]
factors of 9 \[=3\times 3\]
So, in all 3 numbers the highest common factor is only digit 3. So, HCF of 3, 6, 9 is 3. Thus, don’t mix up this HCF as the answer of LCM is 18.