How to Convert Between Kilometers, Miles, and Other Long Distance Units
The LCM of 8 and 12 is a basic yet essential concept in mathematics, especially when dealing with multiples, fractions, and common denominators. Knowing how to find the Least Common Multiple (LCM) is helpful for school exams, competitive tests, and even daily calculations that involve matching or grouping numbers.
What is the LCM of 8 and 12?
The LCM (Least Common Multiple) of two numbers is the smallest positive integer that is a multiple of both numbers. For 8 and 12, the LCM is the smallest number that both 8 and 12 can divide without leaving a remainder.
LCM of 8 and 12 is 24.
This is because 24 is the first number that appears in both the list of multiples of 8 (8, 16, 24, 32, ...) and 12 (12, 24, 36, 48, ...).
Methods to Find LCM of 8 and 12
There are several ways to find the LCM of 8 and 12. Below are the most common methods:
1. Prime Factorization Method
-
Write the prime factors:
- 8 = 2 × 2 × 2 = 23
- 12 = 2 × 2 × 3 = 22 × 3
-
Choose the highest power of each prime:
- Highest power of 2: 23
- Highest power of 3: 31
-
Multiply them together:
- LCM = 23 × 3 = 8 × 3 = 24
2. Division (Ladder) Method
- Write both numbers side by side: 8, 12
- Divide by common prime factors until all that's left is 1:
| Step | Operation | Results |
|---|---|---|
| 1 | Divide by 2 | 4, 6 |
| 2 | Divide by 2 again | 2, 3 |
| 3 | Divide by 2 (for the 2 only) | 1, 3 |
| 4 | Divide by 3 | 1, 1 |
Multiply all divisors: 2 × 2 × 2 × 3 = 24
3. Listing Multiples
- Multiples of 8: 8, 16, 24, 32, 40, ...
- Multiples of 12: 12, 24, 36, 48, ...
- The smallest common multiple is 24.
Worked Examples
Let's use the above methods in practice:
Example 1: Find the LCM of 8 and 12 by Prime Factorization
- Prime factors of 8: 2 × 2 × 2
- Prime factors of 12: 2 × 2 × 3
- LCM = 23 × 3 = 8 × 3 = 24
Example 2: List Multiples to Find LCM
- Multiples of 8: 8, 16, 24, 32...
- Multiples of 12: 12, 24, 36...
- Common multiples: 24, 48, ...
- Smallest is 24.
Example 3: Relationship Between GCF and LCM
GCF of 8 and 12 is 4. The product of the GCF and LCM should equal the product of the original two numbers.
GCF × LCM = 8 × 12 → 4 × 24 = 96
8 × 12 = 96 (Verified!)
Practice Problems
- Find the LCM of 4 and 6.
- What is the LCM of 8, 12, and 16?
- If a number is a common multiple of 8 and 12, name three possible values.
- What is the greatest common factor (GCF) of 8 and 12?
- Write the first 5 common multiples of 8 and 12.
Common Mistakes to Avoid
- Confusing LCM with GCF — LCM is about the least common multiple (bigger number), GCF is about greatest common factor (smaller).
- Missing prime factors when finding the LCM using prime factorization. Always use the highest powers in either number.
- Choosing the first multiple you see, instead of checking which is the smallest common one.
Real-World Applications
The concept of LCM is used in real life to solve synchronization problems, such as finding a time when two repeating events coincide, or to find a common time interval for scheduling. For example, if one bus arrives every 8 minutes and another every 12 minutes, both will arrive together every 24 minutes. LCM is also useful in maths problems involving fractions, algebra, or even in areas like computing and engineering when working with cycles and periodic tasks.
At Vedantu, we help students understand topics like LCM and GCF through interactive examples, worksheets, and video tutorials.
In summary, the LCM of 8 and 12 is 24. Knowing how to find it can help you solve maths problems easily, especially in topics like fractions, word problems, and even real-world scheduling. Practice different methods, avoid common mistakes, and remember—learners succeed when they understand the basics well!
Explore more number theory concepts at Vedantu to improve your problem-solving confidence for both school and competitive exams.
FAQs on Which Units Are Commonly Used to Measure Long Distances?
1. What units are used to measure long distances?
The most common units for measuring long distances are the kilometer (km) in the metric system and the mile (mi) in the imperial system. Other units, like the nautical mile, are used in specific fields like navigation.
2. What is longer: a kilometer or a mile?
A mile is longer than a kilometer. One mile is approximately equal to 1.609 kilometers.
3. Why is the kilometer used instead of meters for long distances?
Kilometers are used for long distances because they are more manageable than meters. Using meters to describe long distances would result in very large numbers, making them less practical. Kilometers provide a more concise way to represent these measurements.
4. How do you convert kilometers to miles?
To convert kilometers to miles, multiply the number of kilometers by approximately 0.621. For example, 10 kilometers is equal to 10 * 0.621 = 6.21 miles. This conversion uses the relationship 1 kilometer ≈ 0.621 miles.
5. Where is the mile still commonly used?
The mile is still commonly used in the United States and the United Kingdom, as well as in some other countries. You'll frequently see miles used on road signs and in discussions about sports distances.
6. What is the best unit for long distance measurement?
The best unit depends on the context. For most international contexts and scientific applications, the kilometer is preferred due to its widespread use and integration into the metric system. However, in the US and UK, the mile remains common.
7. What measurement is used to measure long distances?
Long distances are measured using units like kilometers and miles. The choice depends on the region and application; however, the metric system (using kilometers) is internationally favored for scientific accuracy.
8. What are long distances measured in?
Long distances are typically measured in kilometers (km) or miles (mi). The nautical mile is another unit used in navigation.
9. What units do you use to measure distance?
The units used to measure distance depend on the scale. For short distances, you might use meters or centimeters. For long distances, kilometers and miles are used. Specialized units exist for astronomical distances.
10. How are these units used in daily life?
Kilometers are commonly used in daily life for measuring distances between cities, road trips, marathon distances, etc. Miles are frequently used in countries like the US and UK for similar purposes. In some specialized applications like aviation or shipping, nautical miles might be used. Understanding these units helps in comprehending information related to travel, sports, and geography.
11. How do I convert km to miles?
To convert kilometers to miles, you multiply the number of kilometers by the conversion factor: 1 kilometer ≈ 0.621 miles.
12. Is 1 mile bigger than 1 km?
Yes, 1 mile is bigger than 1 kilometer. 1 mile is approximately equal to 1.609 kilometers.
