## Unit: 8

__HCF and LCM__

In this unit, we are finding the H.C.F. and L.C.M of algebraic expressions by using factorization method. So, the process to find the factors of algebraic expressions are must important for the factors of the following algebraic expressions in the group.

i) 3x + 6 ii) 2x² – 6x – ax +3a iii) 3x² – 27y²

Can you find the factors of a² – 3a and a² – 9? Also, show the factors of these expressions in Venn-diagrams.

### Highest Common Factor (H.C.F.)

Let us consider two numbers 12 and 42. Find the factors of 12 and 42.

Factors of 12 are 1, 2, 3, 4, 6, 12

Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42

Here, the common factors of 12 and 42 are 1, 2, 3, and 6.

Among these factors, 6 is the highest factor of 12 and 42.

**∴** **6**** ****is the highest common factor of 12 and 42.**

### Lowest Common Multiple (L.C.M)

Let’s consider two numbers 8 and 12.

The multiples of 8(M₈) = 8, 16, 24, 32, 40, 48, 56, 64, 72

The multiples of 12(M₁₂) = 12, 24, 36, 48, 60, 72, 84

What are common multiples of 8 and 12?

The common multiples of 8 and 12 are 24, 48, 72

But the least common multiple of 8 and 12 is 24?

## HCF and LCM Class 10 Maths Solution PDF

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## Is Class 10 Math Guide Helpful For Student ?

I have published this Notes for helping students who can’t solve difficult maths problems. Student should not fully depend on this note for doing all exercises. If you totally depend on this note and simply copy a to z then it may affect your study.

Student should also try to solve some problems themselves. You can use this note as a reference. You should check all the answers carefully because all the answers may not be correct. There may be some minor mistakes in the note, please consider those mistakes.

## How to secure good marks in Mathematics ?

As, you may know I’m also a student. Being a student is not so easy. You have to study and work hard in 8 different subjects. From my point of view most of the student are weak in mathematics. They face difficulties while solving maths problems. I was also facing the same problem when I was in grade 10.

If you also want to secure good marks in mathematics then you should practise them everyday. You should always start your practise from a simple problems. When you solve some simple problems then it will motivates you to solve some other harder problem. Slowly and gradually increase the difficulty of questions day by day.

Maths is not only about practising. You also needs to be clear about the concept of solving the problems. When you get the concept then you can easily solve maths problems which are in similar formats.

You should make the habit of making side notes. It means you should make notes of formulas, tips of solving that problems and the main concept.

When your teacher tries to make the concept clear by giving some random example then all student tries to remember the same example but you shouldn’t do that. You should try to relate that concept with your daily life and create your own formula of remembering the concepts.

If you give proper time for your practise with proper method of practising then you’ll definitely score a good marks in your Exam. You can also make a time table for your study and read accordingly.

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