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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

Respuesta :

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

Notice that -5 fits all these requirements:

[tex]-5\equiv15\mod20[/tex]
[tex]-5\equiv20\mod25[/tex]
[tex]-5\equiv25\mod30[/tex]
[tex]-5\equiv31\mod36[/tex]
[tex]-5\equiv43\mod48[/tex]

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

[tex]\mathrm{lcm}(20,25,30,36,48)=3600[/tex]

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

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