Question 1016489
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A certain number leaves a remainder of 4 when divided by 5, a remainder of 5 when divided by 6, and a remainder of 6 when divided by 7. Find the smallest number that satisfies these conditions.
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Let n be your number.


Add 1 (one) to n.


Then n+1 is multiple of 5, of 6 and of 7.


The smallest integer positive n+1 with such properties is 5*6*7 = 210.


Hence your number n is 210 - 1 = 209. 


See the lesson <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.