Find the smallest three digit positive integer which when divided by 2 gives remainder 1, when divided by 3 gives remainder 2, when divided by 4 gives remainder 3 and when divided by 5 gives remainder 4.

Sure, here is the step by step solution:

Step 1: We know that the smallest three-digit positive integer is 100. So, we start from 100.

Step 2: We need to find a number which gives a remainder of 1 when divided by 2, a remainder of 2 when divided by 3, a remainder of 3 when divided by 4, and a remainder of 4 when divided by 5.

Step 3: We start checking each number from 100 onwards to see if it meets the above conditions.

Step 4: The first number we find that meets these conditions is 101.

101 divided by 2 gives a remainder of 1. 101 divided by 3 gives a remainder of 2. 101 divided by 4 gives a remainder of 1, which does not meet our condition. So, we move to the next number.

Step 5: We continue this process until we find a number that meets all the conditions.

Step 6: The smallest three-digit positive integer that meets all these conditions is 119.

119 divided by 2 gives a remainder of 1. 119 divided by 3 gives a remainder of 2. 119 divided by 4 gives a remainder of 3. 119 divided by 5 gives a remainder of 4.

So, the smallest three-digit positive integer which when divided by 2 gives remainder 1, when divided by 3 gives remainder 2, when divided by 4 gives remainder 3 and when divided by 5 gives remainder 4 is 119.