Question

The pairs of natural numbers whose least common multiple is $78$ and the greatest common divisor is $13$ are:

Answer 1

Solution.

Let us consider that natural numbers are $m\mathrm{and}n$.

As we know,

$$\begin{gathered} \mathrm{LCM}\times \mathrm{GCD}=\mathrm{product}\mathrm{of}\mathrm{two}\mathrm{numbers} \\ 78\times 13=\mathrm{m}\times \mathrm{n} \\ 1014=\mathrm{m}\times \mathrm{n} \end{gathered}$$

If $m=13$, $n=\frac{1014}{13}=78$

If $m=3$, $n=\frac{1014}{3}=338$

Hence, the pair of numbers are $(13,78)\mathrm{and}(3,338)$.