Question

The product of the LCM and HCF of two num-
bers is 24. The difference of the two numbers
is 2. Find the numbers.
(b) and​

Answer 1

Answer:

This will surely help you

Answer 2

Solution :

Let the two number be r and m respectively.

A/q

$\longrightarrow\rm{r-m=2}\\\\\longrightarrow\rm{r=2+m.......................(1)}$

&

We know that;

$\boxed{\bf{Product\:of\:two\:numbers=H.C.F\times L.C.M}}}}$

$\longrightarrow\rm{rm=24}\\\\\longrightarrow\rm{(2+m)m=24\:\:[from(1)]}\\\\\longrightarrow\rm{2m+m^{2} =24}\\\\\longrightarrow\rm{m^{2} +2m-24=0}\\\\\longrightarrow\rm{m^{2} +6m-4m-24=0\:\:\:[factorise]}\\\\\longrightarrow\rm{m(m+6)-4(m+6)=0}\\\\\longrightarrow\rm{(m+6)(m-4)=0}\\\\\longrightarrow\rm{m+6=0\:\:\:Or\:\:\:m-4=0}\\\\\longrightarrow\rm{\pink{m\neq -6\:\:Or\:\:m=4}}$

Putting the value of m = 4 in equation (1),we get;

$\longrightarrow\rm{r=2+4}\\\\\longrightarrow\rm{\pink{r=6}}$

Thus;

The two number will be 6 and 4 .