To find the least common multiple (LCM) of 12 and 9, we can list their multiples and find the smallest multiple they have in common:
Multiples of 12: 12, 24, 36, 48, 60, ...
Multiples of 9: 9, 18, 27, 36, 45, 54, 63, ...
We can see that the smallest multiple they have in common is 36. Therefore, the LCM of 12 and 9 is 36.
Alternatively, we can use the prime factorization method to find the LCM:
Prime factorization of 12: 2^2 x 3
Prime factorization of 9: 3^2
To find the LCM, we need to take the highest power of each prime factor that appears in either number. In this case, the highest power of 2 is 2^2, and the highest power of 3 is 3^2. Therefore, the LCM of 12 and 9 is 2^2 x 3^2 = 36.