When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value of n?

Solution:

We know by Euclid's division lemma that

Dividend = [integer quotient] × divisor + remainder

n = 3p + 2

n = 5q + 1

Where p and q are the quotients

Substitute the values of p and q as 0, 1, 2, 3 …..

n = 3p + 2

If p = 0, n = 3(0) + 2 = 2

If p = 1, n = 3(1) + 2 = 5

If p = 2, n = 3(2) + 2 = 8

If p = 3, n = 3(3) + 2 = 11

n = 5q + 1

If p = 0, n = 5(0) + 1 = 5

If p = 1, n = 5(1) + 1 = 6

If p = 2, n = 5(2) + 1 = 11

The common value of n is 11

Therefore, the least possible value for n is 11.

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When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. What is the least possible value of n?

Summary:

When the positive integer n is divided by 3, the remainder is 2 and when n is divided by 5, the remainder is 1. The least possible value of n is 11.