Question

Write all the numbers less than $100$ which are common multiples of $3$ and $4$.

Answer 1

The numbers less than $100$ which are common multiples of $3$ and $4$.

Let us take the LCM of $3$ and $4$

Prime factorization of $3$:

$3=1\times 3$

Prime factorization of $4$:

$4=1\times 2\times 2$

Therefore,

$$\begin{gathered} \mathrm{LCM}\left(3,4\right)=1\times 2\times 2\times 3 \\ =12 \end{gathered}$$

Now, the multiples of $12$ are the common multiples of $3$ and $4$which are less than $100$ are:

$12,24,36,48,60,72,84,96$

Thus, numbers less than $100$ which are common multiples of $3$ and $4$ are $12,24,36,48,60,72,84,96$.