SOLUTION: What least number, when divided by 26,36 and 56, leaves the remainders 6,16,36 respectively ? A. 6588 B. 6552 C. 6532 D. 6536

Algebra ->  Equations -> SOLUTION: What least number, when divided by 26,36 and 56, leaves the remainders 6,16,36 respectively ? A. 6588 B. 6552 C. 6532 D. 6536      Log On


   

Question 1041463: What least number, when divided by 26,36 and 56, leaves the remainders 6,16,36 respectively ?
A. 6588
B. 6552
C. 6532
D. 6536
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
N= the number we are looking for.
Since N divided by 26 leaves the remainder 6 ,
N=26q%2B6 where q is a non-negative integer that is the quotient of N divided by 26 .
N=26q%2B6 means N%2B20=26q%2B6%2B20=26q%2B26=26%28q%2B1%29 ,
so N%2B20 is a multiple of 26 .
If N divided by 36 yields the quotient p and leaves the remainder 16 ,
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=56m%2B36, and N%2B2=56m%2B36%2B20=56m%2B56=56%28m%2B1%29 is a multiple of 56 .
So, N%2B20 is a common multiple of 26 , 36 , and 56 .
The least positive N%2B20 is the least common multiple of
26-2%2A13 , 36=4%2A9 and 56=4%2A14=2%2A4%2A7 , which is
2%2A4%2A7%2A9%2A13=56%2A9%2A13=6552 ,
so the least N is N=6552-20=highlight%286532%29 .