What is the least common multiple of 9 and 6?
The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both of them. To find the LCM of 9 and 6, we can list the multiples of each number until we find the smallest common multiple, or we can use the prime factorization method.
Let's find the LCM of 9 and 6 using the prime factorization method:
First, express each number as a product of its prime factors:
9 = 3^2
6 = 2 × 3
Next, for the LCM, take the highest power of each prime that appears in the factorization of either number:
LCM(9, 6) = 2 × 3^2
Now, multiply those prime factors together:
LCM(9, 6) = 2 × 3^2 = 2 × 9 = 18
So, the least common multiple of 9 and 6 is 18.