What is the least positive integer that has a remainder of 0 when divided by 2, a remainder of 1 when divided by 3, and a remainder of 2 when divided by 4?
I need to find a number that is divisible by 2, but not by 3 or 4. That means it must be even, but not a multiple of 4 or 6. The smallest even number is 2, but that has a remainder of 2 when divided by 3, not 1. The next even number is 4, but that has a remainder of 0 when divided by 4, not 2. The next even number is 6, but that has a remainder of 0 when divided by 3, not 1. The next even number is 8, but that has a remainder of 0 when divided by 4, not 2. The next even number is 10, and that works! It has a remainder of 0 when divided by 2, a remainder of 1 when divided by 3, and a remainder of 2 when divided by 4. So the least positive integer that satisfies the conditions is 10. 