What is the LCM of 12 and 16?

Least Common Multiple is 48 .
Explanation:
Multiples of 12 are ${\displaystyle \{12,24,36,48,60,72,84,96,108,\dots \}}$
Multiples of 16 are ${\displaystyle \{16,32,48,64,80,96,112,\dots \}}$
Hence, common multiples are ${\displaystyle \{48,96,\dots \dots \dots ..\}}$

and Least Common Multiple is 48 .

Explanation:
Think about the multiples of 12 since it is the lesser of the two numbers. That is 12 times (2,3,4,5,6,7,8,9). When the larger number 16 divides exactly into one of the multiples of 12 then that is the LCM.
${\displaystyle \star }$ Can 12 be divided exactly by 16 ? No - so not 12.
${\displaystyle \star }$ Can 24 be divided exactly by 16 ? No - so not 24.
${\displaystyle \star }$ Can 36 be divided exactly by 16 ? No-so not 36.
${\displaystyle \star }$ Can 48 be divided exactly by 16 > Yes 3 times.
${\displaystyle \Rightarrow 48}$ is the LCM of 12 and 16

Explanation:
Each number should be written as the sum of its prime factors. then you are aware of the situation.
$16=2\times 2\times 2\times 2=2^4$
$12=2\times 2\times 3=2^2\times 3$
The LCM must be contain all of the prime factors, but without unnecessary duplicates.
$LCM=2^4\times 3=16\times 3=48$
This is the same method which is used in Algebra.