It reminds me nothing in particular that I can remember
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169 is the smallest such number.
5.5
23 is an odd number between 10 and 30 that gives a remainder of 2 when divided by 7.
Yes, if divided by 2 it gives a whole number of 34
The numbers divided by 5 gives 1 remainder means it should end either 1 or 6. But in case of number ends with 6 will be divided by 2. So only number ending with 1 have to consider. Also the number should be divisble by 7. So when number ending with 3 is multiplied by 7 will give result of number ending 1. So, possibilities are 7*3, 7*13, 7*23, etc In that least number which solves this problem 7*43 = 301. So the least possible number is 301.