Sure, let's solve the two parts of the given question step-by-step.
### (a) Largest Measuring Can for Oil Containers
We are asked to determine the largest measuring can that can exactly measure oil from both the 16-liter and 24-liter containers. This problem can be solved by finding the Greatest Common Divisor (GCD) of the two volumes.
#### Steps:
1. Identify the Volume of Containers:
- Container 1: 16 liters
- Container 2: 24 liters
2. Compute the Greatest Common Divisor (GCD):
- The GCD of 16 and 24 is the largest number that can divide both 16 and 24 without leaving a remainder.
Thus, the largest measuring can that can exactly measure oil from both the containers is 8 liters.
### (b) Smallest Length of a Room for Carpets
We need to find the smallest length of a room that can exactly fit carpets of length 12 meters and 9 meters. This problem can be solved by finding the Least Common Multiple (LCM) of the two lengths.
#### Steps:
1. Identify the Lengths of the Carpets:
- Carpet length 1: 12 meters
- Carpet length 2: 9 meters
2. Compute the Least Common Multiple (LCM):
- The LCM of 12 and 9 is the smallest number that is a multiple of both 12 and 9.
Thus, the smallest length of a room that can exactly fit carpets of length 12 meters and 9 meters is 36 meters.
### Summary:
- The largest measuring can for 16-liter and 24-liter containers is 8 liters.
- The smallest length of a room that can fit carpets of 12 meters and 9 meters in length is 36 meters.
