Question

Is it possible to have two numbers whose HCF is 16 and LCM is 860?Give reason.

​

Answer 1

We have to assume two numbers first.

Given that the HCF of two numbers is 16.  Thus let two numbers be 16x and 16y where x and y are coprime integers.

$\begin{tabular}{c|l}16& 16x,\ 16y \\ \cline{2-}& x,\ y \\ \cline{2-}\end{tabular}$

From the method we get that the HCF is 16 as we mentioned earlier, and the LCM is 16xy, which is equal to 860 as mentioned in the question.

$\displaystyle \begin{aligned}&16xy=860\\ \\ \Longrightarrow\ \ &xy=\frac{860}{16}\\ \\ \Longrightarrow\ \ &xy=53.75\end{aligned}$

Here we get that the value of xy is 53.75, which is not an integer.

As xy is not an integer, then neither is x nor is y.

Thus there are no possible integers whose LCM and HCF are 860 and 16 respectively.