HCF and LCM Calculator
HCF:
LCM:
HCF Calculator: What is HCF and LCM and how to calculate
HCF (Highest Common Factor) and LCM (Least Common Multiple) are two important concepts of mathematics that help in solving fraction, multiplication, and division problems. These concepts are used in most mathematical problems, such as finding divisibility, converting numbers to common multiples, and simplifying fractions. In this article, we will give detailed information about the uses, advantages, results, formulas, tables, examples, and methods of using the calculator of HCF and LCM.
HCF (Highest Common Factor)
What is HCF?
HCF is the largest numerical factor of two or more numbers that can divide those numbers. It is also called GCD (Greatest Common Divisor).
Uses of HCF
To find the fraction of two or more numbers in their simplest form.
To understand divisibility in mathematical problems.
To divide numbers into their common factors.
Benefits of HCF
Simple and fast solution to problems.
Increasing accuracy in mathematical calculations.
Presenting numbers in simplest form.
HCF extract formula
The following methods are used to extract HCF:
euclidean method:
For two numbers a and b, where a > b,
HCF(a, b) = HCF(b, a % b) until b = 0.
prime factorization method:
Write the prime factors of all the numbers.
Take the common prime factor with the lowest exponent and multiply them.
LCM (Least Common Multiple)
What is LCM?
LCM is the smallest multiple of two or more numbers that can divide those numbers exactly.
Uses of LCM
In finding common factors for different numbers.
In making the fractions equal.
In time and distance problems.
Benefits of LCM
Bringing problems to a common solution.
Simplifying calculations of fractions and multipliers.
Solving mathematical problems.
Formula to find LCM
The following methods are used to find LCM:
prime factorization method:
Write the prime factors of all the numbers.
Take the highest exponent of all prime factors and multiply them.
formula method:
LCM(a, b) = (a × b) / HCF(a, b)
Table of HCF and LCM
Example
Example of HCF
Suppose we have to find the HCF of 48 and 60:
Prime Factorization:
48 = 2^4 × 3
60 = 2^2 × 3 × 5
Common prime factors: 2^2 and 3
HCF = 2^2 × 3 = 4 × 3 = 12
Example of LCM
Suppose we have to find the LCM of 12 and 15:
Prime Factorization:
12 = 2^2 × 3
15 = 3 × 5
Maximum exponents of all prime factors: 2^2, 3^1, 5^1
LCM = 2^2 × 3^1 × 5^1 = 4 × 3 × 5 = 60
Using HCF and LCM Calculator
Method
Open the calculator.
Enter the numbers for which HCF or LCM is to be calculated.
Click on the “Calculate” button.
Look at the result.
