"Shortcut to find HCF and LCM" is the one which ever student is looking for. Because, often some people find it difficult to find HCF and LCM. At that time they are in need of the easiest way to find HCF and LCM. That is nothing but the shortcut to find HCF and LCM.
HCF and LCM shortcut has been developed using venn diagram from the topic "Sets" in math. The picture given below clearly illustrates the easiest way to find HCF and LCM of two numbers.
To get the easiest way (shortcut) to find HCF and LCM of two numbers, we have to be
knowing the following steps explained.
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 = 2x2x2x3
60 = 2x2x3x5
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).
Hence H.C. F of 24 and 60 = 2x2x3 = 12
L.C.M = Multiply all the prime factors which are found in the two circles (Including the prime factors in the common region)
Hence L.C.M of 24 and 60 = 2x2x2x3x5 = 120
having seen the steps explained in the above problem of HCF and LCM, we hope that the students will not find it difficult to find H.C.F and L.C.M of two numbers.
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