Question

Find the biggest three-digit no. which when divided by 2,3,4,5,6,9& 15 ,gives the reminder as 1 every time.​

Answer 1

Here (3-1) =2

Here (3-1) =2(4-2) =2 , (5-3)= 2, (6-4) =2 and (7-5) =2

Here (3-1) =2(4-2) =2 , (5-3)= 2, (6-4) =2 and (7-5) =2 LCM of 3, 4, 5, 6, 7 is 420.

Here (3-1) =2(4-2) =2 , (5-3)= 2, (6-4) =2 and (7-5) =2 LCM of 3, 4, 5, 6, 7 is 420.Consider three digit number 999

Here (3-1) =2(4-2) =2 , (5-3)= 2, (6-4) =2 and (7-5) =2 LCM of 3, 4, 5, 6, 7 is 420.Consider three digit number 999When 999 is divided by 420, the remainder is 159 with quotient 2.

Here (3-1) =2(4-2) =2 , (5-3)= 2, (6-4) =2 and (7-5) =2 LCM of 3, 4, 5, 6, 7 is 420.Consider three digit number 999When 999 is divided by 420, the remainder is 159 with quotient 2.Subtracting 159 from 999 gives 840.

Here (3-1) =2(4-2) =2 , (5-3)= 2, (6-4) =2 and (7-5) =2 LCM of 3, 4, 5, 6, 7 is 420.Consider three digit number 999When 999 is divided by 420, the remainder is 159 with quotient 2.Subtracting 159 from 999 gives 840.again subtract 2 from 840 = 838. {here 2 is subtracted from 840 as the difference between the given divisors and the remainders is 2 in each case)

Here (3-1) =2(4-2) =2 , (5-3)= 2, (6-4) =2 and (7-5) =2 LCM of 3, 4, 5, 6, 7 is 420.Consider three digit number 999When 999 is divided by 420, the remainder is 159 with quotient 2.Subtracting 159 from 999 gives 840.again subtract 2 from 840 = 838. {here 2 is subtracted from 840 as the difference between the given divisors and the remainders is 2 in each case)Now,when 838 is divided by 3, 4, 5, 6, 7 we get the remainders as 1, 2, 3, 4, 5 respectively.

Here (3-1) =2(4-2) =2 , (5-3)= 2, (6-4) =2 and (7-5) =2 LCM of 3, 4, 5, 6, 7 is 420.Consider three digit number 999When 999 is divided by 420, the remainder is 159 with quotient 2.Subtracting 159 from 999 gives 840.again subtract 2 from 840 = 838. {here 2 is subtracted from 840 as the difference between the given divisors and the remainders is 2 in each case)Now,when 838 is divided by 3, 4, 5, 6, 7 we get the remainders as 1, 2, 3, 4, 5 respectively.Hence only one such number is possible.