HCF and LCM of Numbers

The concepts of Highest Common Factor (HCF) and Least Common Multiple (LCM) are crucial components of the Quantitative Aptitude section in the Common Law Admission Test (CLAT). These concepts involve understanding the relationship between numbers and their divisors, which is essential for solving various mathematical problems. In this article, we will delve into the fundamental concepts of HCF and LCM, provide examples to illustrate these concepts and offer strategies to solve problems effectively.

Understanding HCF and LCM Basics

HCF and LCM are two mathematical concepts that play a significant role in solving problems involving multiples and divisors.

1. Highest Common Factor (HCF): The HCF of two or more numbers is the largest number that divides all of them without leaving a remainder. It is also known as the greatest common divisor (GCD).

2. Least Common Multiple (LCM): The LCM of two or more numbers is the smallest multiple that is divisible by all of them.

Solving HCF and LCM Problems: Concepts and Examples

Example 1: Finding HCF

Question: Find the HCF of 36 and 48.

Solution:

List the factors of each number:

– Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

– Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The largest number that appears in both lists is 12. Therefore, the HCF of 36 and 48 is 12.

Example 2: Finding LCM

Question: Find the LCM of 15 and 25.

Solution:

List the multiples of each number:

– Multiples of 15: 15, 30, 45, 60, …

– Multiples of 25: 25, 50, 75, 100, …

The smallest number that appears in both lists is 75. Therefore, the LCM of 15 and 25 is 75.

Strategies for Solving HCF and LCM Problems

Solving problems related to HCF and LCM requires careful analysis and systematic approaches. Here are some strategies to help you tackle these problems effectively:

1. Prime Factorisation Method: Decompose the numbers into their prime factors. The HCF will be the product of the common prime factors raised to the lowest powers, while the LCM will be the product of all prime factors with the highest powers.

2. Divisibility Rules: Utilise the divisibility rules to quickly identify common factors and multiples.

3. List Method: List the factors or multiples of the given numbers and identify the common elements.

4. Using Formulas: For two numbers, HCF × LCM = Product of the two numbers. This formula can help you solve problems involving HCF and LCM relationships.

5. Practice Regularly: Regular practice of HCF and LCM problems will enhance your familiarity with the concepts and improve your problem-solving speed.

Conclusion

Understanding HCF and LCM is essential not only for the CLAT but also for various mathematical applications in real life. With a solid grasp of these concepts and consistent practice, you can confidently approach problems that involve finding common factors and multiples. Embrace prime factorisation, use divisibility rules, apply systematic methods and remember the formulas to efficiently solve HCF and LCM problems.

As you prepare for the CLAT, mastering these concepts will enhance your mathematical abilities and boost your overall confidence in tackling competitive exams. So, arm yourself with the knowledge of HCF and LCM and approach quantitative problems with precision and skill!