​If LCM (p, q, r) = 420, HCF (p, q, r) = 1, HCF (p, q) = 3, HCF (q, r) = 5 and HCF (p, r) = 1, then the product of p, q and r is what ? ? ?  ?  ?  ?

really need help please answer as soon as possible . . . . . . .

Answer :

Given :  LCM ( p, q , r ) =  420  , HCF ( p , q , r ) = 1, HCF ( p , q ) = 3 , HCF ( q , r ) = 5 and HCF ( p , r ) = 1

And
420 = 2 $\times$ 2 $\times$ 3 $\times$ 5 $\times$  7 
And

As given HCF ( p , q ) = 3 , So

p =  3 $\times$ (  Some more numbers )
And
q = 3 $\times$ ( Some more numbers )

HCF ( q , r ) = 5 , So

q =  3 $\times$ 5
And
r = 5 $\times$ ( Some more numbers )

And

HCF ( p , r ) = 1 ,  So

p =  3 $\times$ 1
And
r = 5 $\times$ 1 ,

But LCM of p ,  q  ,  r  =  420  and 420   =  2 $\times$ 2 $\times$ 3 $\times$ 5 $\times$ 7  , So

p = 3 $\times$ 1 $\times$ 2 $\times$ 2 
q  = 3 $\times$ 5
And
r =  5 $\times$ 7 , So

p =  12  , q  =  15 and r =  35 , So

p $\times$ q  $\times$ r  =  12 $\times$ 15 $\times$ 35  =  6300                                                                           ( Ans )