a three digit no when divided by 5 leaves remainder 3 and when divided by 7 leaves remainder of 5.when it is added to 2 it is divisible 9. find the smallest 3 digit no that fits this situation
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In this question, we are given
Remainder from 6 is 5
Remainder from 5 is 3
So, the number N = LCM(6,5)*n + constant = 30n + constant
To figure out the constant, look at the numbers which give a remainder of 5 from 6.
They are 5, 11, 17, 23, 29....
Among these, find the one which leaves a remainder of 3 from 5. It is 23.
So, our number N should be of the format of 30n + 23
Biggest three digit number will occur when n is 32 = 30*32 + 23 = 983
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