HOW TO FIND HCF AND LCM EASILY

How to Find HCF and LCM Easily :

In this section, we will learn, how to find the highest common factor and least common multiple of two or more numbers. 

HCF and LCM Here we are going to see how to find highest common factor.

We can find H.C.F any two or more numbers using ladder diagram method.

Now we can see the steps to be followed while using ladder diagram method to find H.C.F and L.C.M of any two or more numbers.

Step 1 : 

Put the given numbers inside the "L" shape 

Step 2 :

We have to split the given number by prime numbers only. That is,  always we have to put prime numbers out side the "L" shape.

Given below will be helpful to find the prime number which exactly divides the given number.

• A number which ends with 0, 2, 4, 6 and 8 is divisible by the smallest prime number 2.
• A number which ends with 0 or 5 is divisible by 5 
• If the sum of digits of the given number is a multiple of 3, then the given number is divisible by 3.

Step 4 :

Repeat this process until get prime numbers inside the ladder.

Step 5 :

The product of numbers out side the ladder will be the H.C.F

Step 6 :

The product of numbers inside and out side the ladder will be the L.C.M

How to Find HCF and LCM Easily - Examples

Example 1 :

Find the H.C.F and L.C.M of 90 and 30.

Solution :

To find the H.C.F and L.C.M of 90 and 30, let us write these two numbers inside the "L" shape.

Example 2 :

Find the H.C.F and L.C.M of 105 and 60.

Solution :

To find the H.C.F and L.C.M of 105 and 60, let us write these two numbers inside the "L" shape.

Example 3 :

Find the H.C.F and L.C.M of 30 and 50.

Solution :

To find the H.C.F and L.C.M of 30 and 50, let us write these two numbers inside the "L" shape.

Example 4 :

Find the H.C.F and L.C.Mr of 80 and 60.

Solution :

To find the H.C.F and L.C.M of 80 and 60, let us write these two numbers inside the "L" shape.

Example 5 :

Find the H.C.F and L.C.M of 36 and 27.

Solution :

To find the H.C.F and L.C.M of 36 and 27, let us write these two numbers inside the "L" shape.

Example 6 :

Find the H.C.F and L.C.M of 75 and 45.

Solution :

To find the H.C.F and L.C.M of 75 and 45, let us write these two numbers inside the "L" shape.

Example 7 :

Find the H.C.F and L.C.M of 36 and 72.

Solution :

To find the H.C.F and L.C.M of 36 and 72, let us write these two numbers inside the "L" shape.

Example 8 :

Find the H.C.F and L.C.M of 72 and 63.

Solution :

To find the H.C.F and L.C.M of 72 and 63, let us write these two numbers inside the "L" shape.

Example 9 :

Find the H.C.F and L.C.M of 120 and 90.

Solution :

To find the H.C.F and L.C.M of 120 and 90, let us write these two numbers inside the "L" shape.

Example 10 :

Find the H.C.F and L.C.M of 45 and 135.

Solution :

To find the H.C.F and L.C.M of 45 and 135, let us write these two numbers inside the "L" shape.

After having gone through the stuff given above, we hope that the students would have understood, how to to find HCF and LCM easily. 

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