Question

Find the least common multiple (LCM) of 9 and 6.A. 54B. 36C. 18D. 3

Answer 1

The LCM of 9 and 6 is 18, therefore the answer is C.

To determine this we can use the prime factorization method.

First we need to find all the prime factors of each number:

$\begin{gathered} 6=2\times3 \\ 9=3\times3 \end{gathered}$

Now for each prime factor we need to find where it occurs most often in the prime factorization and we need to write that many times in a list. In this case we have two prime factors: 2 and 3. 2 appears once at the prime factorization of six and 3 appears twice at the prime factorization of 9, then our list is:

2, 3, 3.

Now we need to multiply the numbers in that list to find the LCM:

$2\cdot3\cdot3=18$

and then the LCM is 18.