Question
The greatest number of four digits which when divided by
10, 12, 14 leave remainders 5, 7, 9 respectively is:Solution
The difference between divisor and the corresponding remainder is equal (i.e 5). LCM of 10, 12 and 14 = 420 Largest 4-digit number = 9999 After dividing 9999 by 420 we will get the remainder as 339. Therefore, the number divisible by 420 = 9999 – 339 = 9660 If 5 is subtracted from the number 9660 the resulting number will follow the condition in the question and that number is 9655.
The least number which when divided by 7, 12, 15 and 20 leave zero remainder in each case and when divided by 26 leaves a remainder of 4 is:
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