Question

find the least natural numbers larger than 100 which leaves the remainder 12 when divided by 19

Answer 1

The answer for this question is 107

Answer 2

Given:

Divisor = 19

Remainder = 12

To find:

The least natural numbers larger than 100 which leaves the remainder 12 when divided by 19.

Solution:

Natural numbers are positive integers greater than or equal to 1.

N = {1,2,3,4,...}

Multiple of 107 are 19, 38, 57, 76, 95, 114,...

It is clear that 95 is the multiple of 19 which immediate less than 100.

Now, add remainder 12 in 95 to get the required number because we want the least natural numbers larger than 100 which leaves the remainder 12 when divided by 19.

$95+12=107$

Therefore, the required number is 107.