# SHORTCUT TO FIND HCF AND LCM

Shortcut to find HCF and LCM :

In this section, we will learn the shortcut to find HCF and LCM.

Here, the shortcut to find HCF and LCM is using Venn diagram.

Using Venn diagram is the easiest way to find the highest common factor and least common multiple of two or more numbers.

## Shortcut to Find HCF and LCM - Example

Problem :

Find the HCF and LCM of 24 and 60.

Solution :

Here is the shortcut to find HCF and LCM of 24 and 60.

That is, using Venn diagram.

Venn diagram shown below clearly illustrates, how to find HCF and LCM of 24 and 60 easily.

## Shortcut to find HCF and LCM - Steps

Step  1 :

We have to decompose the given numbers in to prime factors.

In the example shown above, we have the two numbers 24 and 60.

24  =  2 x 2 x 2 x 3

60  =  2 x 2 x 3 x 5

Step 2 :

Now, we have to draw two circles as shown above. The first one is for 24 and the second one is for 60.

Step 3 :

In the prime factors of 24 and 60, strikeout the common factor (which is found in both 24 and 60) and write that one in common region (intersection part) of two circles.

Step 4 :

If we find a prime factor which is in 24 but not in 60, strikeout that one and it has to be written in the circle of 24 (not in the common region).

If we find a prime factor which is in 60 but not in 24, strike out that one and it has to be written in the circle of 60 (not in the common region).

This process has to be continued until all the prime factors of both 24 and 60 are struck out.

Step 5 :

Once all the prime factors of both 24 and 60 are struck out, we have to do the following works to get HCF and LCM.

H.C.F  =  Multiply the prime factors which are found in the common region (Intersection part).

So, the H.C.F of 24 and 60 is

=  2 x 2 x 3

=  12

L.C.M  =  Multiply all the prime factors which are found in the two circles (Including the prime factors in the common region)

So, the L.C.M of 24 and 60 is

=  2 x 2 x 2 x 3 x 5

=  120

1. Find the HCF and LCM of 18 and 24.

2. Find the HCF and LCM of 36 and 42.

3. Find the HCF and LCM of 45 and 54.

4. Find the HCF and LCM of 9 and 15.

5. Find the HCF and LCM of 64 and 88.

After having gone through the stuff given above, we hope that the students would have understood the shortcut to find the highest common factor and least common multiple of two or more numbers.

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