$LCM(3,5)=15$ Ans $=[\frac{2013}{15}]+[\frac{2013}{15^2}]+[\frac{2013}{15^3}]+...=134+8+0+0...=142 $

3 or 5 means $ =[\frac{2013}{3}]+[\frac{2013}{5}]-[\frac{2013}{15}]= 671+402-134=969$ my english not Good but i understand 3 or 5 like this if im wrong can anybody explain redoxs solution?

byrmc wrote: 3 or 5 means $ =[\frac{2013}{3}]+[\frac{2013}{5}]-[\frac{2013}{15}]= 671+402-134=969$ my english not Good but i understand 3 or 5 like this if im wrong can anybody explain redoxs solution? You are correct. Redox might have misread the problem...he is finding the powers of 15 but he is neglecting individual $5's$ and $3's$ which can make more $15's$.k However, this is not what the problem asked....

Actually, byrmc is not completely correct $671+402-134=\boxed{939}$ But this problem is very very easy and I'd expect it in the middle school contest.