find the least common multiple (lcm) of 12 and 9.

Explanation:

Step1: Prime - factorize the numbers

$12 = 2^2\times3$; $9 = 3^2$

Step2: Determine the highest - power factors

For the prime factor 2, the highest power is $2^2$. For the prime factor 3, the highest power is $3^2$.

Step3: Calculate the LCM

$LCM(12,9)=2^2\times3^2 = 4\times9=36$

Answer:

36