document.write( "Question 1132855: What is the least positive integer meeting each of the following conditions?
\n" ); document.write( "Dividing by 7 gives a remainder of 4.
\n" ); document.write( "Dividing by 8 gives a remainder of 5.
\n" ); document.write( "Dividing by 9 gives a remainder of 6. \n" ); document.write( "

Algebra.Com's Answer #750004 by MathLover1(20850) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "Notice that the difference in each of those cases is $\"3\"$ . ( $\"7-4\"$ , $\"8-5\"$ , $\"9-6\"$ ) \r
\n" ); document.write( "\n" ); document.write( "Ask yourself what would happen if you added $\"3\"$ to this number? \r
\n" ); document.write( "\n" ); document.write( "Well, when you divided the new number by $\"7\"$ , you would get a remainder of $\"7\"$ , which means $\"no\"$ remainder. Same thing for $\"8\"$ and $\"9\"$ . \r
\n" ); document.write( "\n" ); document.write( "So this new number is a common multiple of $\"7\"$ , $\"8\"$ , and $\"9\"$ . And because you are looking for the $\"least\"$ $\"+positive\"$ integer, the new number must be $\"7%2A8%2A9=504\"$ .
\n" ); document.write( "Since we added $\"3\"$ to the number, we have to subtract $\"3\"$ to get the number you are looking for, $\"501\"$ . \r
\n" ); document.write( "\n" ); document.write( "check:\r
\n" ); document.write( "\n" ); document.write( " $\"501\"$ divided by $\"7+=+71\"$ remainder $\"4+\"$
\n" ); document.write( " $\"501+\"$ divided by $\"8+=+62\"$ remainder $\"+5+\"$
\n" ); document.write( " $\"501\"$ divided by $\"9+=+55\"$ remainder $\"6\"$ \r
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