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mafiozo [28]
3 years ago
8

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

Mathematics
1 answer:
Otrada [13]3 years ago
5 0
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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