Find the Unique Number

Can you find the least possible number such that

If the number is divided by 3, it gives the remainder of 1;
If the number is divided by 4, it gives the remainder of 2;
If the number is divided by 5, it gives the remainder of 3;
If the number is divided by 6, it gives the remainder of 4.




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Can you calculate the total time each of the insects took to change their positions?

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* *
x *
=====
* * *

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Can you find out the remainder when 3^300 is divided by 5?

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