Question

30.
The difference between the LCM and HCF of the natural numbers n and bis 57. What is the minimum
value of n +b?
(A)22
(B)27
(C)31
(D) 58​

Answer 1

Step-by-step explanation:

Let us suppose that HCF of two natural numbers a and b be h.

Then a= hx and b= hy where x and y are coprimes.

LCM(a,b) = hxy

Given that LCM(a,b)- HCF(a,b)= 57

Or hxy-h=57

If h=1 then xy =58

It gives x=2,y=29 so a=2,b=29 ,sum=31

If h=3 then xy =20

It gives x=4,y=5 so a=12,b=15, sum=27

Minimum value of a+b is 27

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