7. (5 points) A number when divided by 5 leaves a remainder of 2, when divided by 6 leaves a remainder of 2, and when divided by 7 leaves a remainder of 3. Find the smallest natural number that satisfies these three conditions


【Answer】Solution: Since a number leaves a remainder of 2 when divided by 5, and also leaves a remainder of 2 when divided by 6, subtracting 2 from this number makes it divisible by 5 and 6. Therefore, this number can be expressed as $30n+2$. Since this number leaves a remainder of 3 when divided by 7, the smallest such number is 122. Therefore, the answer is 122.