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

Answer:

36

Explanation:

Step1: Prime - factorize the numbers

$9 = 3\times3$; $12=2\times2\times3$

Step2: Determine the highest - power factors

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

Step3: Calculate the LCM

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