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Solve the following:

(a) Two containers have 16 L and 24 L of oil. What is the largest measuring can that can exactly measure oil from both the containers?

(b) What is the smallest length of a room in which an exact number of carpets of length 12 meters and 9 meters can fit?

Sagot :

GinnyAnsweridn
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.
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