HCF and LCM – Quantitative Aptitude

Quantitative Aptitude – HCF and LCM

HCF and LCM is one of the most important chapter in Quantitative Aptitude. We all learn HCF and LCM in our school days. These are the basics of math calculations. In competitive exam preparation also we need HCF and LCM very much. So now we will recall what we have learned in our school days.

HCF (Highest Common Factor)

Definition: The largest whole number which is a Factor of two other whole numbers is called HCF.

Let’s explain this,

First of all we need to know What is Factor ?

Factors are Numbers which we multiply to get another number. For example,

2 and 5 are the Factors of 10. Because, 2 X 5 = 10.
Similarly 3 and 4 are Factors of 12 (3 X 4 = 12).

But we can also do this, 2 X 6 = 12. So, 2 and 6 are also factors of 12.
So, 1, 2, 3, 4, 6 and 12 itself are factors of 12.

 

Now we will find out HCF of two numbers using above rule.

Let’s take 12 and 18 and find out the HCF of these two numbers. So, First of all we need to find out the factors of these two numbers.

Factors of 12 are : 1, 2, 3, 4, 6 and 12.
Factors of 18 are : 1, 2, 3, 6, 9 and 18.

So, common factors between these two numbers are: 1, 2, 3 and 6. And the largest common factor between these two number is 6. So, HCF of 12 and 18 is 6.

 

LCM (Least Common Multiple)

Difinition: The smallest whole number which is divisible by two other whole number is called LCM.

Let’s explain this,

First of all we need to know What is Multiple of a Number ?

It’s very easy, Multiple of a number is the product of that number with any counting numbers. For example,

Multiples of 5 are : (5 X 1) = 5, (5 X 2) = 10, (5 X 3) = 15, (5 X 4) = 20, (5 X 5) = 25, (5 X 6) = 30, …

 

Now we will find out LCM of two numbers using above rule.

Let’s take 12 and 18 again and find out the LCM of these two numbers. So, First of all we need to find out the multiples of these two numbers.

Multiples of 12 are : 12, 24, 36, 48, 60, 72, 84, 96, …
Multiples of 18 are : 18, 36, 54, 72, 90, 108, 126, …

So, common multiples between these two numbers are: 36, 72 and many more. But we need only the smallest common multiples between these two numbers. And the smallest common multiple between these two number is 36. So, LCM of 12 and 18 is 36.

 

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