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What is the least possible number which ...

What is the least possible number which when divided by 13 leaves the remainder 3 and when it is divided by 5 it leaves the remainder 2.

Text Solution

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Let the required number be N then it can be expressed as follows
N = 13k + 3 .........(i)
and N = 5l + 2 .....(ii)
where k and l are the quotients belong to the set of integers.
Thus 5l + 2 = 13k + 3 `rArr` 5l - 13k = 1 `rArr` 5l = 13k + 1 `rArr` l =`(13k + 1)/5`
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