Question 1064777
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<pre>
Let N be our unknown number under the question.


Consider the number N-1.


According to the condition, it is multiple of 2, 3, 4, 5 and 6.
Hence, N-1 is the multiple of 60.


It means that our N is somewhere among these numbers: 

60+1, 2*60+1, 3*60+1, 4*60+1, 5*60+1, 6*60+1

i.e, among the numbers 61, 121, 181, 241, 301.


Check, which of these numbers is multiple of 7.
</pre>

<U>Answer</U>. 301.


See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/divisibility/lessons/The-number-that-leaves-a-remainder-1-when-divided-by-2-by-3-by-4-by-5-and-so-on-until-9.lesson>The number that leaves a remainder 1 when divided by 2, by 3, by 4, by 5 and so on until 9</A>

in this site.