Explain LCM and HCF in Detail

H.C.F. and L.C.M. are the abbreviations of Highest Common Factor and Least Common Multiple, respectively. The greatest factor present between two or more numbers is identified by the H.C.F., while the least number that is exactly divisible by two or more numbers is described by the LCM. The greatest common factor (GCF) is also known as the greatest common factor (HCF), and the least common divisor (LCM) is also recognized as the least common divisor. The Prime factorization method and the division method are two important methods for determining H.C.F. and L.C.M. Both techniques were taught in previous classes. The division method is a quick way to find both H.C.F. and L.C.M. Let’s use a formula to learn about the relationship between HCF and LCM. We will also solve several problems based on these two ideas to better understand them.

What is HCF?

HCF is also named as the greatest common divisor, or gcd, of two or more positive integers, is the largest positive integer that divides the numbers without leaving any remainder or answer behind, according to the mathematical properties. Considering the numbers 8 and 12. Since the maximum number that can divide both 8 and 12 is 4, the H.C.F. of 8 and 12 would be 4.

How to Find HCF?

There are various easy and manageable ways to find the highest common factor of the given numbers on a number line. Irrespective of the method to find the HCF the answer to the HCF of the numbers will always be the same and exact. There are 3 different methods to calculate the HCF of two numbers on a number line:

  • HCF by listing out the common factors of the number
  • HCF by the prime factorization method
  • HCF by the division method
What is LCM?

The least common multiple, or LCM, of two numbers, say a and b, is denoted as LCM in arithmetic (a,b). The least positive integer that is divisible by both a and b is expressed as the LCM.

How to obtain the Least Common Multiple?

LCM of numbers of a provided number set can be obtained by the use of various manageable methods. There are 3 different methods to know and obtain the least common multiple of two or more numbers. Below are the primary methods to find the LCM.

  • LCM by the listing Method
  • LCM by the aid of prime factorization
  • LCM by the use of the division method
Properties of LCM and HCF
  1. The product of LCM and HCF of any two given natural numbers on a number line is equivalent to the obtained product of the given numbers.
  2. The HCF of co-prime numbers is invariably 1. Therefore, the LCM of given co-prime numbers on a number line is equal to the product of the given numbers.
  3. HCF of any number set in a number system is never greater than any of the other given numbers.
  4. LCM of any two or more numbers on a number line is never smaller than any of the other given numbers.
Relationship Between LCM and HCF

The highest common factor of a set of numbers is the HCF of the given numbers. It is determined by multiplying the given numbers’ common prime factors. The smallest number among all common multiples of the given numbers is the least common multiple of two or more numbers, while the least common multiple is the smallest number among all common multiples of the numbers. Let us assume ‘x’ and ‘y’ are the two numbers on a number line then the formula that gives the relationship between their LCM and HCF is stated as: LCM of (x,y) × HCF of (x,y) give us: x × y.

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