Question

What is the LCM of $5$, $8$ and $9$?

Answer 1

Hint: From the given question we are asked to find the least common multiple of two given numbers. Here for this question, we will use the prime factorisation method and find the factors for the two given numbers and then we find the least common multiple for the numbers given. So, we proceed with our solution as follows.

Complete step-by-step solution:
Generally, the prime factorisation which is breaking down a given number into its prime (meaning a number only divisible by itself and \[1\]) factors (meaning the numbers which you multiply in order to get a certain product).
The number $5$ breaks down into $5$ and$1$. Which cannot be further divided.
So, the factorisation will be as follows.
$\Rightarrow 5=5\times 1$
Then number 8 breaks down into ${{2}^{3}}$. Which cannot be further divided.
So, the factorisation will be as follows.
$\Rightarrow 8={{2}^{3}}$
The number $9$ breaks down into $3$ and $3$. Which cannot be further divided.
So, the factorisation will be as follows.
 $\Rightarrow 9=3\times 3$
The, multiply the factors by the most number of times they appear in either set of factors.
Therefore, there are no common factors, we have to multiply all the factors of $5$, 8 and $9$.
Now, we multiply all those factors of the given numbers together which gives us the LCM.
$\Rightarrow LCM=5\times {{2}^{3}}\times 3\times 3\times 1$
$\Rightarrow LCM=360$
Therefore, LCM of $5$, 8 and $9$ is $360$

Note: Students should have good knowledge in the concept of prime factorisation and also the concept of LCM. If we take the three and two only one time and multiply together, we get $ LCM=5\times 2\times 3\times 1$ instead of $ LCM=5\times {{2}^{3}}\times 3\times 3\times 1$ it makes our solution wrong.