Question 543190: Hi,
Kindly provide the solution for this below mentioned problem?
Find the largest 5-digit number which when divided by 84, 72 and 96 leaves remainder 82, 70, and 94 respectively.
Regards
Gopinath
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The key to solving this problem is to realize that your mystery number is 2 short of a multiple of 84, 72, and 96. If we call your mystery number  , then  is a multiple of 84, 72, and 96.
The least common multiple of 84, 72, and 96 is
If the problem just asked for any "number which when divided by 84, 72 and 96 leaves remainder 82, 70, and 94 respectively," we would say that  , with  would be one of many solutions. All the solutions would be numbers such that
 for some positive integer  .
As the problem asks for "the largest 5-digit number," we need to look for an multiple of 672 that makes the largest 5-digit number complying with the condition.
 according to my calculator, so I can easily estimate that  will yield a 5-digit , while the next larger multiple of 672  will yield a 6-digit
In other words,  is the solution.
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