GMAT Min/Max Problem

If 7(a – 1) = 17(b – 1), and a and b are both positive integers the product of which is greater than 1, then what is the least possible sum of a and b?

A. 2
B. 7
C. 17
D. 24
E. 26

17 is not divisible by 7 which means that b-1 must be divisible by 7. 

So, b — 1 = 7*something . 

least value of b is 8.

Also, 7 is not divisible by 17. 

(a -1 ) is must be the multiple of 17. 

So the least value of a = 18 and the least value of a + b = 18 + 8 = 26.

E