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# Need help

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252
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Find the smallest positve $n$ such that:

\begin{align*}
N &\equiv 6 \pmod{12}, \\
N &\equiv 6 \pmod{18}, \\
N &\equiv 6 \pmod{24}, \\
N &\equiv 6 \pmod{30}, \\
N &\equiv 6 \pmod{60}.
\end{align*}

May 11, 2018

### Best Answer

#3
+1

Melody:

The smallest N is 6. The LCM of[12, 18, 24, 30, 60] = 360. Therefore:

N = 360k + 6, where k = 0, 1, 2, 3.........etc.

May 11, 2018

### 4+0 Answers

#1
+982
+1

Hey Guest!

\begin{align*} N &\equiv 6 \pmod{12}, \\ N &\equiv 6 \pmod{18}, \\ N &\equiv 6 \pmod{24}, \\ N &\equiv 6 \pmod{30}, \\ N &\equiv 6 \pmod{60}. \end{align*}

LCM [12, 18, 24, 30, 60] = 360

N = 360k + 6.

6 is your answer.

Guest is right, my previous answer was wrong.

I hope this helped,

gavin

May 11, 2018
edited by GYanggg  May 12, 2018
#2
+101725
+1

The smallest N is 6, the rest of my answer was incorrect.

May 11, 2018
edited by Melody  May 12, 2018
#3
+1
Best Answer

Melody:

The smallest N is 6. The LCM of[12, 18, 24, 30, 60] = 360. Therefore:

N = 360k + 6, where k = 0, 1, 2, 3.........etc.

Guest May 11, 2018
#4
+101725
0

Yes you are right ....

I appologise for my incorrect answer :)

Melody  May 12, 2018