Question

$\huge\bf{Question}$

What is LCM and HCF?
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Note:- Neat answer
Proper Answer​

Answer 1

Answer:

The full forms of H.C.F. and L.C.M. are, Highest Common factor and Least Common Multiple, respectively. The H.C.F. defines the greatest factor present in between given two or more numbers, whereas L.C.M. defines the least number which is exactly divisible by two or more numbers.

Answer 2

★ Solution :-

HCF and LCM are a common terms used mathematics for different algebraic questions. For beginners who are introduced to algebraic operations it is necessary to know what is HCF and LCM and to work upon them.

Let's know about them.

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• LCM ::

LCM stands for the abbreviation of Least Common Multiple. Least Common Multiple means the number which smallest among the common multiples of a certain group of numbers. This LCM can be found out using Prime Factorisation or Direct Multiplication.

→ Prime Factorisation Method :

In this way we take out the prime Factorisation of the given numbers and multiply them the prime factors of both numbers with each in their highest common power.

For example :-

Let's take two numbers as 12 and 6

On taking prime Factorisation, we get

> 12 = 2 × 2 × 3 = 2² × 3¹

> 6 = 2 × 3 = 2¹ × 3¹

We see that 3¹ is the highest degree for 3 and common term in prime Factorisation of both. But we see that in prime Factorisation of 12 we 2² and for 6 we have 2¹. So in such cases, we will take the term with highest degree. This is a more precise method.

> LCM(12, 6) = 2² × 3¹ = 12

This means LCM of 12 and 6 is 12.

• Direct Multiplication Method :

In this method, in order to obtain LCM we directly multiply the given numbers.

For example :-

Let's take two numbers as 11 and 10.

Then,

> LCM (11, 10) = 11 × 10 = 110

This is means LCM of 11 and 10 is 110 .

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• HCF ::

HCF stands for the abbreviation of Highest Common Factor. It is also referred as Greatest Common Divisor (GCD). Both are same terms only. HCF is the product lowest degree prime numbers or greatest common number among the factors of the given group of numbers which can divide the numbers in the group. This can be found out by Prime Factorisation method.

• Prime Factorisation :

In this way firstly we can take out the prime factorisation of the give numbers and then multiply all the prime factors with minimum degrees to get a number which will be the HCF of given numbers.

For example :-

Let's take two numbers as 10 and 20.

By prime factorisation we can get,

> 10 = 2 × 5 = 2¹ × 5¹

> 20 = 2 × 2 × 5 = 2² × 5¹

Here we see that 5¹ is a common term in prime factorisation of both numbers which is there in its lowest degree. And also we 2¹ is the minimum degree for the term 2. So HCF will be given as,

> HCF (10, 20) = 2¹ × 5¹ = 10

This means HCF of 10 and 20 is 10.

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• Facts about LCM and HCF ::

• Though by name HCF has the term highest but it is always smaller than the LCM which has term as lowest

• HCF is used to find the constant of ratios mostly.

• LCM is used to solve fractions mostly.

• LCM takes highest degrees of prime multiples.

• HCF takes lowest degree of prime multiples.