HOW TO FIND HCF AND LCM EASILY

In this section, you will learn how to find highest common factor (HCF) and Least common multiple (LCN) two or more numbers using ladder method.

The following steps will be useful to find HCF and LCM of two or more numbers using ladder method. .

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 HCF

Step 6 :

The product of numbers inside and out side the ladder will be the LCM

Example 1 :

Find the HCF and LCM of 90 and 30.

Solution :

To find the HCF and LCM of 90 and 30, let us write these two numbers inside the L shape.

Example 2 :

Find the HCF and LCM 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 HCF and LCM 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 HCF and LCM 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 HCF and LCM 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 HCF and LCM 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 HCF and LCM 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 HCF and LCM 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 HCF and LCM 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 HCF and LCM 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.

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