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Question 85

The least number that is to be subtracted from 2580 so that it leaves a remainder 4 when divided by 9, 11 and 13 is

Solution

The question asks for a number which will leave remainder 4 whether it is divided by 9 or 11 or 13.
The number has to be less than 2580 and largest possible in this range.

This means that the desired number will be of the form = k*(LCM of 9,11,13) + 4
where K means any multiple of the LCM of 9,11,13 and should result in a number less than 2580
LCM if 9, 11, 13 is 1287. For k = 2, we get the desired number as = 2574 + 4 = 2578
Hence, 2 must be subtracted from 2580 to get desired number.

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