document.write( "Question 1041463: What least number, when divided by 26,36 and 56, leaves the remainders 6,16,36 respectively ? \r
\n" ); document.write( "\n" ); document.write( "A. 6588
\n" ); document.write( "B. 6552
\n" ); document.write( "C. 6532
\n" ); document.write( "D. 6536 \n" ); document.write( "

Algebra.Com's Answer #656435 by KMST(5328) $\"\"$ $\"About$

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$\"N\"$ = the number we are looking for.
\n" ); document.write( "Since $\"N\"$ divided by $\"26\"$ leaves the remainder $\"6\"$ ,
\n" ); document.write( " $\"N=26q%2B6\"$ where $\"q\"$ is a non-negative integer that is the quotient of $\"N\"$ divided by $\"26\"$ .
\n" ); document.write( " $\"N=26q%2B6\"$ means $\"N%2B20=26q%2B6%2B20=26q%2B26=26%28q%2B1%29\"$ ,
\n" ); document.write( "so $\"N%2B20\"$ is a multiple of $\"26\"$ .
\n" ); document.write( "If $\"N\"$ divided by $\"36\"$ yields the quotient $\"p\"$ and leaves the remainder $\"16\"$ ,
\n" ); document.write( " $\"N=36p%2B16\"$ , and $\"N%2B20=36p%2B16%2B20=36p%2B36=36%28p%2B1%29\"$ is a multiple of $\"36%29%29%29+.%0D%0AIf+%7B%7B%7BN\"$ divided by $\"56\"$ yields the quotient $\"m\"$ and leaves the remainder $\"36\"$ ,
\n" ); document.write( " $\"N=56m%2B36\"$ , and $\"N%2B2=56m%2B36%2B20=56m%2B56=56%28m%2B1%29\"$ is a multiple of $\"56\"$ .
\n" ); document.write( "So, $\"N%2B20\"$ is a common multiple of $\"26\"$ , $\"36\"$ , and $\"56\"$ .
\n" ); document.write( "The least positive $\"N%2B20\"$ is the least common multiple of
\n" ); document.write( " $\"26-2%2A13\"$ , $\"36=4%2A9\"$ and $\"56=4%2A14=2%2A4%2A7\"$ , which is
\n" ); document.write( " $\"2%2A4%2A7%2A9%2A13=56%2A9%2A13=6552\"$ ,
\n" ); document.write( "so the least $\"N\"$ is $\"N=6552-20=highlight%286532%29\"$ .
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