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I did not quite understand the question itself. must be.. is the tricky thing for me, you asked whether it can be solved within 2 minutes time, it can be if my answer is correct.
at least n should be 35, It is the LCM. if lets say n is 35 then it cannot be divided by 70 or 12. so not necessarily n should be devisible by 70 and 12 if it is divisible by 7 and 5.