Question

How do you find the $LCM$ and $GCF$ (of two or more numbers) using prime factorization?

Answer 1

How to find the LCM and GCF:

For $\text{GCF}$ find the prime numbers that are shared in common and multiply.

For example $15$ and $20$

$$\begin{gathered} 15=3\times 5 \\ 20=2\times 2\times 5 \end{gathered}$$

There are shared factors of $5$, so the GCF is $5$.

For $\text{LCM}$ find prime numbers that are different that are not shared and multiply.

There are only one $3$ in $15$, so there are one $3$ that are not shared.
There are only one $5$ in $15$ and only one $5$ in $20$, so there are one $5$ that are not shared.

There are two $2$ in $20$, so there are two $2$ that are not shared.

Therefore, the LCM is in below :

$2\times 2\times 3\times 5=60$