Question

if the LCM of three numbers is 9570 then their hcf will be

Answer 1

Thanks for the interesting question!

Let us consider three numbers as 9570, 1 and 1.
Therefore, LCM = 9570,  HCF = 1


Now if we consider three numbers as 9570, 9570 and 9570.
Then, LCM = 9570,   HCF = 9570

But in the above-mentioned question, choices have already been given and we are supposed to eliminate values which can not be HCF.

Upon, prime factorization of 9570, we get solution as 

9570 = 2*3*5*11*29 

And we know that HCF must always be a factor of LCM. 
So from the given choices in the question itself, only 11 can be the HCF.

Hence, 11 is the answer.

Hope it helps!