What is the result of multiplying the greatest common factor of $30$ and $102$ by the least common multiple of $12$ and $15$?

The correct option is A $360$
First, determine the prime factors of $30$ and $102$:
$30=2\times 3\times 5$,
$102=2\times 3\times 17$.
To find the greatest common factor of two numbers, multiply all prime factors that the numbers have in common.

The greatest common factor of $30$ and $102$ is therefore $2\times 3=6$.

An easy way to find the least common multiple of two numbers is to look at the multiples of the largest number until you find a multiple of the smallest number.

Here, we need to look at the multiples of $15$ until we find a multiple of $12$.

Now, $15,30$, and $45$ arent divisible by $12$, but $60$ is, so $60$ is the least common multiple of $12$ and $15$.

The answer is: $6\times 60=360$.