The least common multiple of the real numbers $8$ and $12$ should be evaluated by the common multiple method in this problem.

Now, let’s learn how to find the lowest common multiple of the integers $8$ and $12$ by using the common multiple method in mathematics.

Firstly, let’s find the multiples of the natural number $8$ and its multiples are written mathematically as follows.

$M_8$ $\,=\,$ $8,$ $16,$ $24,$ $32,$ $40,$ $48,$ $56,$ $64,$ $72,$ $80,$ $\cdots$

Similarly, find the multiples of the whole number $12$ and its multiples are expressed mathematically in the following way.

$M_{12}$ $\,=\,$ $12,$ $24,$ $36,$ $48,$ $60,$ $72,$ $84,$ $96,$ $108,$ $\cdots$

Now, let’s compare the multiples of the numbers $8$ and $12$ to identify the commonly appearing multiples.

$M_8$ $\,=\,$ $8,$ $16,$ $\color{blue}{24},$ $32,$ $40,$ $\color{blue}{48},$ $56,$ $64,$ $\color{blue}{72},$ $80,$ $\cdots$

$M_{12}$ $\,=\,$ $12,$ $\color{blue}{24},$ $36,$ $\color{blue}{48},$ $60,$ $\color{blue}{72},$ $84,$ $96,$ $108,$ $\cdots$

The numbers $24,$ $48,$ $72$ and so on are appeared commonly in the multiples of the numbers $8$ and $12$. The number $24$ is a small number in the list of the commonly appearing multiples of the $8$ and $12$.

Therefore, it is evaluated that the number $24$ is the LCM of the numbers $8$ and $12$ by using the common multiple method.

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