Q. 1.5 - Intermediate Algebra

Question

Find the LCM of 9 and 12 using the Prime Factors Method. 

Step-by-Step Solution

Answer

The LCM of 9 and 12 is 36.

Step 1. Given information

The given numbers are 9 and 12.

We have to calculate the LCM of the given numbers using the prime factorization method.

Step 2. Prime factorize 9 and 12

Now,

$\Rightarrow 9=3\times 3$

and,

$\begin{array}{l}\Rightarrow 12=2\times 6\\ \Rightarrow 12=2\times 2\times 3\end{array}$

Step 3. Calculating the LCM.

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.
Thus,

$\begin{array}{l}\Rightarrow \mathrm{LCM}=2\times 2\times 3\times 3\\ \Rightarrow \mathrm{LCM}=4\times 9\\ \Rightarrow \mathrm{LCM}=36\end{array}$