I had asked the below question before also, but the expert answer by providing me with a weblink which was just a little similar to my asked query but was not much proper. 
So, I request the expert to get into this query again.
QUESTION:

Find the greatest number of five digits which is divisible by 56, 72, 84 and 96 leaves reminders 48, 64, 76 and 88 respectively. ​

Dear Student,

Please find below the solution to the asked query:

To find greatest number of five digits which is divisible by 56, 72, 84 and 96 leaves reminders 48, 64, 76 and 88 respectively. ​

We find difference between each number with their respective remainder :

56 - 48 = 8 ,

72 - 64 = 8 ,

84 - 76 = 8 ,

96 - 88 = 8 ,

Here we can see that we have common difference = 8 

Now we find L.C.M. of 56 , 72 , 84 and 96  , As :

56 = 2 × 2 × 2 × 7 ,

72 = 2 × 2 × 2 × 3 × 3 ,

84 = 2 × 2 × 3 × 7 ,

96 = 2 × 2 × 2 × 2 × 2 × 3

L.C.M. ( 56 , 72 , 84 and 96 ) = 2 × 2 × 2 × 2 × 2 × 3 × 3 × 7 = 2016

And we know highest 5 digit number  = 9999

And

999992016 = 4912152016
So,

Greatest number of five digits which is divisible by 56, 72, 84 and 96  =  49 × 2016 = 98784

Therefore,

Greatest number of five digits which is divisible by 56, 72, 84 and 96 leaves reminders 48, 64, 76 and 88 respectively = 98784 - 8 = 98776                                         ( Ans )


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