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The number should end with a unit digit of either 2 or 7. Therefore, the number when divided by 11 should end in 4 or 9 on which 8 should be added to get the number N. Such number is 162. The next number should be 162+165 and so on
YOur approach is less time consuming. In such questions, observation is very much required like the one you have made out: N required 3 only to be divisible by 3,5,11. LCM comes handy here. I tried with LCM but then could not use your observation.Therefore, used the other method.
HBS: Reimagining Capitalism: Business and Big Problems : Growing income inequality, poor or declining educational systems, unequal access to affordable health care and the fear of continuing economic distress...