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Question 1132855: What is the least positive integer meeting each of the following conditions?
Dividing by 7 gives a remainder of 4.
Dividing by 8 gives a remainder of 5.
Dividing by 9 gives a remainder of 6.
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
Notice that the difference in each of those cases is  . ( ,  ,  )
Ask yourself what would happen if you added to this number?
Well, when you divided the new number by  , you would get a remainder of , which means  remainder. Same thing for  and  .
So this new number is a common multiple of , , and . And because you are looking for the   integer, the new number must be  .
Since we added to the number, we have to subtract to get the number you are looking for,  .
check:
divided by  remainder 
 divided by  remainder
divided by  remainder 
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