Hi All , today we will study about HCF And LCM. It is also one of the important topic of quantitative aptitude.

Before starting this topic we will take a short quiz based on the numbers system and discuss a simple way to find the square of 30-130 numbers within 10 seconds.

**So , here we start with the quiz:-**

I hope you all scored 100% in above quiz. Now as i mentioned , we will learn a simple way to find square of numbers ranging between 30-130. For this you should know squares of numbers ranging between 1-30.

**For Numbers Ranging between 70-130**

When you are going to find squares between 70-130 then take base as **“100”**. Now for example you have to find square of number 102. Then our base is 100. Now find out difference between 100 and 102. In this case the difference is of 2.

So add 2 in 102 and we will get the new number as 104. Now find out square of 2 that is 4 and add it to last two places. Add 4 to 10400. Now someone may ask why we add two 0’s . we added two 0’s because the last two unit digits of 100 are 0.

Therefore** square of 102 is 10404.**

Now lets find out square of 119. The difference between 100 and 119 is 19 . so we add 19 in 119. As a result of this we get 138 as new number. Now square of 190 is 361, add this 361 into last two places. **13800 + 361 = 14161**

Now lets find out **square of 78.**

The difference between 100 and 78 is of 22. Now we will subtract 22 from 78. So the new number will be 56. Now add square of 22 in its last two unit places. **5600+484=6084.**

**For Numbers Ranging between 30-70**

Take base as 25 and sub base as 50. Now for example we need to find square of 66. The difference between 50 and 66 is of 16. so we further add 16 in 25. so the new number is 41. Now find square of 16 and add it into last two unit digit places of 41. 4100+ 256=4356.

Lets find square of 39. the difference between 50 and 39 is 11. so subtract 11 from 25 and we will get new number as 14. Now add 11’s square in last two unit digit places of 14. 1400+121=1521.

Below questions are assignment for you. In case you have some doubt or need some clarification then do contact me on my email id [email protected]

**HCF And LCM**

**HCF**:

Highest Common factor (HCF) of two numbers is the greatest number , which divides each of them exactly. HCF is also known as Greatest Common Divisor(GCD).

**How to Find HCF:**

**HCF by Factorisation** **method:**

In this method, express each one the given numbers as the product of prime numbers. The product of prime factors common to all the numbers will be the HCF.

For example: **Find HCF of 30,60 and 90**.

Factors of 30=2*3*5

60=2*2*3*5

90=2*3*3*5

Therefore product of common prime factors with the least powers = 2*3*5=30.

Therefore 30 is the HCF of the above question.

#### HCF by division method:

Divide the greater number by smaller number. Now divide the divisor by remainder , repeat this process till the remainder is zero. Then the last divisor is the required HCF.

**For example:**

**Find HCF of 48,72**

In this question the **HCF is 24.**

**LCM**

Least Common Multiple (LCM) of two or more numbers is the least number which is divisible by each of these numbers.

**How to Find LCM:**

**LCM by Factorisation Method**

Write the given numbers into their prime factors. Then the product of terms of highest powers of all the factors is the required LCM.

For Example: **Find the LCM of 12,15 and 18**.

Factors of 12= 2*2*3

15=3*5

18=2*3*3

LCM=*2 ^{2}**

*3**5=2*2*3*3*5=180.

^{2}#### LCM by Division Method:

We will know about this method by following example.

**Find LCM of 4,8 and 12.**

Factors are 2*2*2*3=24. So LCM of the above question is 24.

**How to calculate LCM and HCF of Fractions?**

LCM of Fraction= LCM of Numerators/HCF of Denominators

HCF of Fraction= HCF of Numerators/LCM of Denominators

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

Questions on the basis of number system and HCF And LCM. In next post we will start with simplifications. Please try to solve these questions.

- T
**he LCM of two numbers is 225 and their HCF is 5. If one number is 25, the find the other number.** **The LCM of two numbers is 495 and their HCF is 5. If the sum of numbers is 100 then find their difference.****Find LCM of 36,72,144,180.****The HCF of two numbers is 8. Which one of the following can never be their LCM: 1.)24 2.) 48 3.) 56 4.)60****Find square of 128 and 63.****Find the number 145875596 is divisible by 3 or not?****The sum of first 50 odd natural numbers will be?****Find the sum of first 50 even natural numbers?**

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Thankss alot mam