VENN DIAGRAM METHOD FOR  HCF AND LCM

Venn diagram can be used to find the highest common factor (HCF) and least common multiple (LCM) of two or more numbers. 

Example :

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.

hcfandlcm.png

The following steps will be useful to find hcf and lcm using venn diagram.

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. 

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

So, the HCF of 24 and 60 is 

= 2 x 2 x 3

= 12

LCM = Multiply all the prime factors which are found in the two circles (Including the prime factors in the common region)

So, the LCM of 24 and 60 is 

= 2 x 2 x 2 x 3 x 5

= 120

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