The LCM of two numbers is 48 and their HCF is 8. If one number is 16, then find the other number.

​The least common multiple is the smallest number which is exactly divisible by both the given numbers.

The highest common factor of two numbers is the largest possible number which divides both the numbers exactly without any remainder.

Answer: If the LCM of 2 numbers is 48 and their HCF is 8 and if one of the numbers is 16, then the other number is 24.

Explanation:

There is a simple empirical formula connecting both LCM and HCF with the numbers.

The formula is LCM (a,b) x HCF (a, b) = a × b

The product of LCM and HCF is equal to the product of the given numbers.

Here,

\begin{eqnarray}\text{LCM} &=& 48\\\\
\text{HCF}  &=& 8\\\\
\text{a} &=&16\\\\
\text{b} &=& ?\\\\\end{eqnarray}

We need to find the other number.

Let us substitute the known values in the above-mentioned formula.

\begin{eqnarray}\text{LCM } \times \text{HCF} &=& \text{a}\times\text{b}\\\\
48 \times 8 &=& 16 \times \text{b}\\\\
\implies\text{b} &=& \frac{(48 \times 8)}{16}\\\\
\implies\text{b} &=& \frac{384}{16}\\\\
\therefore\text{b} &=& 24\end{eqnarray}

So, the other number, denoted by b, is 24.

Thus, If the lcm of two numbers is 48 and their HCF is 8 and one number is 16, then the other number is​ 24.