​Let r be the greatest number which when divides 41, 71 and 91 leaves the same remainder. Find the LCM of r and 45.

Correct option is B

​Given:
Numbers = 41, 71, 91.

Solution: 

r leaves the same remainder,

So, 
Differences:71 - 41 = 30, 91 - 71 = 20, 91 - 41 = 50.

Now, 
GCD of 30, 20, 50 = 10.

then, 
LCM of 10, 45 = 90 

Thus, the Greatest r = 90