Answered

which smallest number will have 15,20,25,31 nd 43 as reminder respectively when divided by 20, 25, 30, 36,48

please explain the answer you found

Verified Answer :

LammettHash

I assume by smallest number, you're really looking for the smallest positive number.

Notice that -5 fits all these requirements:

\(-5\equiv15\mod20\)
\(-5\equiv20\mod25\)
\(-5\equiv25\mod30\)
\(-5\equiv31\mod36\)
\(-5\equiv43\mod48\)

Any number of the form \(-5+nk\) will also satisfy these conditions, where \(k\in\mathbb Z\) and \(n\) is the least common multiple of the moduli. You have

\(\mathrm{lcm}(20,25,30,36,48)=3600\)

so the least positive number would be achieved with \(k=1\), giving 3595 as the answer. (Verified with a script.)

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