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

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) (Show Source): You can put this solution on YOUR website!
= the number we are looking for.
Since divided by leaves the remainder ,
where is a non-negative integer that is the quotient of divided by .
means ,
so is a multiple of .
If divided by yields the quotient and leaves the remainder ,
, and is a multiple of divided by yields the quotient and leaves the remainder ,
, and is a multiple of .
So, is a common multiple of , , and .
The least positive is the least common multiple of
, and , which is
,
so the least is .

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