Question 1001840

{{{x}}} must be divisible by {{{3}}},{{{4}}},{{{5}}}  
Hence 
{{{x=n*LCM(3,4,5)=n*60}}}  

So {{{x=60n}}} for any integer {{{n}}}.

since the problem asks for the "smallest positive" such number, the answer is:

{{{x=60*1}}} or
{{{ x=60 }}}=> smallest number divisible by {{{3}}},{{{4}}},{{{5}}} 

since we also have reminder of {{{2}}}, your number is

{{{x+2=62}}}

check:

{{{62/3=20}}} and reminder {{{2}}}
{{{62/4=15}}} and reminder {{{2}}}
{{{62/5=12}}} and reminder {{{2}}}