Question

What is the least common multiple of 3 and 9?

Answer 1

Hint: We have to find the least common multiple of 3 and 9, which is abbreviated as LCM. So, we will first find the factors of 3 and 9 using the common division method. Then, we will note down common factors and multiply them to get the LCM.

Complete step by step solution:
We know that the least common multiple of any two numbers is the least number which is exactly divisible by both the numbers. The least common multiple is mostly abbreviated as LCM. We can find the LCM of the given numbers by the help of just listing the multiples or by common division method.
We have to find LCMs 3 and 9.
We will use the common division method. In this method we divide both the numbers by prime numbers together and stop it when the further division of these numbers is not possible with the help of prime numbers and (1,1) left at the end.
Then we just multiply the divisors and this will give the least common multiple of the given numbers.
LCM of 3 and 9;
$\begin{align}
  & 3\left| \!{\underline {\,
  3,9 \,}} \right. \\
 & 3\left| \!{\underline {\,
  1,3 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,1 \,}} \right. \\
\end{align}$

Thus, LCM of 3 and 9 = $3\times 3=9$.

Note: There is another method, the listing multiple method. In this method we will have to list some of the multiples of 3 and 9 and the multiple which is common in both as well as the smallest one if there are more common multiples will be the least common multiple (LCM) of the 3 and 9.
LCM of 3 and 9;
Multiples of 3= 3,6,9,12,15,18 …….
Multiples of 9= 9,18,27…...
Here, we can see that the multiple fulfilling the both criteria (i.e., multiple common in both as well as the smallest one if more common multiples are there) is none other than 9.
Thus, LCM of 3 and 9 = 9.