I am a number between 1 and 100. If you divide me by 3, the remainder is 2. If you divide me by 5, the remainder is 4. If you divide me by 7, the remainder is 6. What number am I?

104

Wait, 104 is greater than 100. Let's find the lowest common multiple of 3, 5, and 7, which is 105. Since the remainders are each 1 less than the divisor (3-1=2, 5-1=4, 7-1=6), the number is LCM(3,5,7) - 1 = 105 - 1 = 104, which is outside 1-100. Let's adjust the question to fit a number below 100: 'What number am I if I am less than 100? Wait, LCM is 105, so the smallest positive is 104. Let's change the question to fit a different set or just state 104 and clarify the range.' Let's use a simpler Chinese Remainder Theorem problem: 'If you divide me by 3, remainder 1. Divide by 4, remainder 2. What is the smallest positive number?' Let's replace with: 'I am a number where dividing by 4 leaves a remainder of 3, and dividing by 5 leaves a remainder of 4. What is the smallest such number?' Answer: 19.