The topics of Least Common Multiple (LCM) and Highest Common Factor (HCF) are extremely important in mathematics. Both are essential concepts in solving algebraic equations, as well as for calculating the greatest common divisor or the greatest common factor. In this article, we will discuss LCM and HCF questions and their solutions.
What is LCM?
Least Common Multiple (LCM) is the smallest number that is a multiple of two or more numbers. It is also referred to as the least common denominator (LCD). To find the LCM of two numbers, you must find the prime factors of each number and then multiply all the common prime factors together. For example, to find the LCM of 12 and 18, you would first find the prime factors of each number. For 12, the prime factors are 2, 2, and 3. For 18, the prime factors are 2, 3, and 3. The LCM of 12 and 18 is then 2 x 2 x 3 x 3, which is equal to 36.
What is HCF?
Highest Common Factor (HCF) is the greatest common divisor of two or more numbers. It is also known as the greatest common factor (GCF). To find the HCF of two numbers, you must first find the prime factors of each number. Then, you must find the greatest common prime factor and multiply it together with the other prime factors. For example, to find the HCF of 12 and 18, you would first find the prime factors of each number. For 12, the prime factors are 2, 2, and 3. For 18, the prime factors are 2, 3, and 3. The HCF of 12 and 18 is then 2 x 3, which is equal to 6.
How to Solve LCM and HCF Questions?
Solving LCM and HCF questions requires the same basic steps. First, you must find the prime factors of each number. Next, you must find the greatest common prime factor (or the least common prime factor, if you are solving an LCM question). Finally, you must multiply the common prime factors together to find the answer.
Solving LCM Questions with Algebra
In some cases, it may be necessary to solve an LCM question using algebra. To do this, you must first express the numbers as the product of two or more prime factors. For example, to find the LCM of 6 and 8, you could express the numbers as 2 x 3 and 2 x 2 x 2, respectively. Then, you must multiply the common prime factors together to find the answer: 2 x 3 x 2 x 2 = 24.
Solving HCF Questions with Algebra
The same basic steps can be used to solve HCF questions using algebra. First, you must express the numbers as the product of two or more prime factors. For example, to find the HCF of 6 and 8, you could express the numbers as 2 x 3 and 2 x 2 x 2, respectively. Then, you must find the greatest common prime factor and multiply it together with the other prime factors: 2 x 3 = 6.
Conclusion
LCM and HCF are important concepts in mathematics, and understanding how to solve LCM and HCF questions is essential for any student studying algebra. By understanding the basic steps for solving these questions, students will be able to quickly and accurately solve any LCM and HCF question that they encounter.
