Question 103

Which is the largest six digit number, which when divided by 12, 15, 20, 24 and 30, leaves the remainders 8, 11, 16, 20 and 26 respectively.

Solution

The LCM of 12, 15 20,24, 30 = 120

the greatest of 6 digit = 999999

Dividing 999999 by 120 we get 39 as the remainder

Hence the 6 digit number divisible by 120 is (999999-39)

= 999960

Since 12-8=4 , 15-11 = 4, 20-16=4, 24-20= 4, 30-26 = 4

then reminder is each case is =4 less then the divior

Hence Requried number

999960-4 = 999956 Ans

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