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Smallest Number


700plus2010

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Approaching these prob is easy if options are given, Neways:

 

Consider the multiple of 7 in each case.

 

7 wil not leave 1 as rem when divided by 8

 

14 wil not leave rem 1 when divided by 2

 

21 wil not leave rem 1 when divided by 6

 

28 wil not give rem 1 when divided by 2 and 4

 

35 wil not give rem 1 when divided by 4

 

42 is divisible by 2 and 6 , hence not possible.

 

49 leaves rem 1 in all cases hence the smallest number is 49.

 

 

Its a bit lengthy method........

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but divides evenly when divided by 7?[/font]

 

 

This essentially means that the number in question is an even multiple of 7 and thus is contradictory to what is presented earlier in the question (as the number will have to be divisible by 2); i guess the question intends to say that the number is perfectly divisible by 7.

 

Another way is to take the LCM of all divisors to which the number yeilds a remiander and add the remainder to this LCM or to any multiple of this LCM, depending on what the question demands.

 

e.g. the LCM of 2, 4, 6 & 8 is as good as the LCM of 6 & 8 = 24 add 1 = 25, but 25 is not a multiple of 7; hence choose 2*24=48+1 = 49 (correct as it is a multiple of 7)

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