Table of Contents
What is the Definition of LCM and HCF?
HCF and LCM – Definition: The LCM (Least Common Multiple) is the smallest number that is a multiple of two or more numbers.
The HCF (Highest Common Factor) is the largest number that is a factor of two or more numbers.
What does HCF mean?
HCF stands for the Highest Common Factor. The Highest Common Factor is the largest number that is a factor of two or more numbers. The Highest Common Factor can be found by dividing all of the numbers by the largest number that is a factor of all of the numbers.
How is HCF calculated?
HCF is calculated by dividing the largest number by the smallest number.
How to calculate LCM and HCF?
The lowest common multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the numbers. The highest common factor (HCF) of two or more numbers is the largest number that is a factor of each of the numbers.
1. Factorization Method
The factorization method is a technique used to solve a system of linear equations. The method works by factoring the coefficients of the equations into a product of linear factors. The factors are then rearranged so that the equations are in standard form and the solution is found by solving the equations.
2. Gaussian Elimination Method
The Gaussian elimination method is a technique used to solve a system of linear equations. The method works by eliminating variables one at a time until the system is in standard form. The solution is found by solving the equations.
3. Prime Factorization Method (Also known as the Factor Tree Method)
- This is a method for finding the prime factors of a number. It is also called the factor tree method because it uses a tree diagram to organize the prime factors.
- To use the prime factorization method, start by writing the number you are trying to factorize vertically. Next, draw a tree diagram with the number at the top and the prime factors below. Write the prime factorization of the number next to the appropriate branch on the tree.
Here is an example.
The number 36 can be factorized into the prime factors 6 and 6.
Here is another example.
The number 15 can be factorized into the prime factors 3 and 5.
Division Method
Let’s say you have the following list of numbers:
1, 2, 3, 4, 5
We can divide this list into two groups:
1, 2, 3, 4, 5
6, 7, 8, 9, 10
The first group is {1, 2, 3, 4, 5} and the second group is {6, 7, 8, 9, 10}.
How to find the HCF of 3 Numbers or How to find the Highest Common Factor?
The Highest Common Factor (HCF) of 3 numbers is the largest number that is a common factor of all 3 numbers.
To find the HCF of 3 numbers, list all of the factors of each number and find the largest number that is a factor of all 3 numbers.
How is LCM Calculated?
- To calculate the LCM, first list all of the multiples of the given number. Next, find the least common multiple (LCM) of all of the multiples. The LCM is the smallest number that is a multiple of all of the given numbers.
- For example, the LCM of 4 and 6 is 12. The multiples of 4 are 4, 8, 12, 16, 20, 24, 28, and 32. The multiples of 6 are 6, 12, 18, 24, 30, 36, 42, and 48. The LCM is 12, because it is a multiple of 4 and 6.
How to find LCM by Prime Factorization?
The LCM can be found by prime factorization. The prime factorization of a number is the decomposition of the number into its prime factors. The prime factors of a number are the numbers that are only divisible by themselves and 1. The LCM can be found by multiplying all of the prime factors of a number together.
How to find LCM by Prime Factorization using the Concept of Exponents?
The LCM of two numbers can be found by multiplying the prime factors of those numbers and then taking the highest power of each prime factor.
Where are HCF and LCM used?
HCF and LCM are used in a variety of different ways. HCF is used to find the greatest common divisor of two numbers, and LCM is used to find the least common multiple of two numbers. These two operations are important in a variety of different mathematical problems, such as finding the solutions to equations. Additionally, HCF and LCM can be used to simplify fractions and to find the prime factors of a number.
