Properties of hcf and lcm

The HCF is the greatest common factor of two or more numbers. The LCM, on the other hand, is the lowest common multiple of these two values. The Greatest Common Factor between any two numbers is also known as HCF. Between two or more numbers, LCM stands for Least Common Divisor.

The prime factorization method and the division method are the two most prevalent methods for calculating HCF and LCM. While the most popular method for calculating HCF and LCM is division. HCF and LCM will be discussed here.

What is the difference between HCF and LCM?

LCM stands for lowest common factor in its full form, whereas HCF stands for highest common factor. The HCF of two or more numbers is the greatest factor, whereas the L.C.M. is the smallest number that is exactly divisible by two or more numbers.

The division method and prime factorization method can be used to find the LCM and HCF of two or more numbers. The division approach, on the other hand, is thought to be the quickest way to find the HCF and LCM. The HCF and LCM are discussed in depth in this article.

What exactly is HCF?

The Highest Common Factor is the full version of HCF. The Greatest Common Factor, or GCD, is another name for HCF (Greatest Common Divisor). The largest positive integer that divides all the provided numbers and leaves 0 is the HCF of a subset of whole numbers.

Multiples and Factors

All the numbers that divide a number completely, without leaving any residue, are called factors. The number 24 can, for example, be divided evenly by 1, 2, 3, 4, 6, 8, 12, and 24. Each of these numbers is a multiple of 24, and they are all factors of 24.

What exactly is a factor?

A number’s factors are the numbers that divide it exactly with no residue. To put it another way, these are the exact divisors of the numbers supplied.

The factors of 20 are, for example, 1,2,4,5,10, and 20.

Let’s look at an example to better understand the notion of HCF:

Consider two figures for HCF: 25 and 20.

As a result, we can see that:

25,25 factors = 1,5,25

20,1,2,4,5,10,20,20,20,20,20,20,20,20,20,20,20,20,20,

The factors of 25 are 1,5 and 25 in this case. Factors of 20 are 1,2,4,5,10,20, and so on. We can claim that 1 and 5 are common factors of both integers in this case. The highest common factor, HCF, is represented by the number 5.

As a result, the number 5 is the highest common factor (HCF) of the numbers 20 and 25.

What exactly is LCM?

The full name of LCM is the lowest common multiple. When two or more integers are multiplied together, the LCM is the number that is divisible by all of them exactly.

Multiples: A number’s multiples are the numbers obtained by multiplying it with any other number.

The first ten multiples of three, for example, will be 3,9,12,15,18,21,24,27, and 30.

Let’s look at how to locate LCM now.

Take the numbers 9 and 12 for example.

The following are 9-digit multiples:

9 times 1 equals 9

18 = 9*2

27 = 9 * 3

36 = 9 * 4

45 = 9*5

Multiples of 12 will be accepted.

12 x 1 = 12.

24 = 12*2

36 = 12 * 3

48 = 12 * 4

60 = 12 * 5

The lowest multiple, which is the common multiple of 9 and 12, is 36, as shown here. As a result, the LCM of the 9 and 12 is 36.

HCF Formula and LCM Formula

The formula for the relationship between HCF and LCM is as follows:

(HCF of the two numbers) x (Product of Two Numbers) (LCM of the two numbers)

According to the formula, if A and B are two numbers, the product of HCF and LCM of two numbers equals the product of the two numbers.

H.C.F.(A,B) x L.C.M.(A,B) = A x B

HCF of two the numbers = Product of the two numbers/LCM of the two numbers

LCM of two the  numbers= Product of the two numbers/HCF of the two numbers

The complete form of HCF and LCM will now be understood. H.C.F. is for Highest Common Factor, and L.C.M. stands for Least Common Multiple.

The following are the properties of HCF and LCM

• Property 1: The product of any two natural numbers’ LCM and HCF is equal to the product of the numbers themselves.

• Property 2: Co-prime numbers have an HCF of 1. As a result, the LCM of the specified co-prime numbers equals the product of the numbers.

• Property 3: The HCF of any two or more numbers can never be bigger than any of the numbers given.

• Property 4: The LCM of any two or more numbers is always greater than one of the issued numbers.

Conclusion

HCF and LCM are essential topics in mathematics because they are useful in solving problems involving time and work, time and distance, pipes and cisterns, and so on. Knowing the L.C.M. and H.C.F. of two or more numbers can help you find rapid solutions and save time on calculations. HCF can be used to solve a variety of mathematical issues, such as determining the largest tape to measure the land, the largest tile size, and so on. Many mathematical issues involving racetracks and traffic lights can be solved using LCM. LCM is also useful in computer science for creating cryptographically encoded messages.