Finding Fast LCM of three or more numbers

Sunday, 23 December 2012

Finding Fast LCM of three or more numbers


Even if we are studying LCM (Least Common Multiple) in our lower classes, We need to apply it in most of the mathematical problems in higher levels and competitive examinations. So here i will explain what is an LCM. How to find the LCM of two or more numbers and finally the technique to find it fast and easily.

LCM is the value,when we take the multiples of two numbers and choose a common multiple of the two numbers which is the least. Looking the figure below you gets the idea.

Lets take two numbers 2 and 8. we list the multiples of both as shown below



So i have marked the common multiples of both the numbers using blue circles and the LCM is the Lowest of that common multiples and here it is 8 and i have marked it with red. So the LCM of 2 and 8 is 8.

similarly i am showing below the LCM of three numbers lets take 4,6, and 8



Here the lowest common multiples of these three numbers is 24.

This is the concept of LCM.

Now we are making a technique to find this fast and easily.
 So we can improve the speed of finding LCM in various entrance tests, bank exams, aptitude tests and all.

This technique will be useful to finding LCM of bigger numbers, so lets take to bigger numbers 24 and 64,so to find LCM for this with new technique ,follow the steps

1. First we find the factors of the terms instead of multiples like shown below


 and find the greatest of that factors(GCF) instead of lowest. That is 8 here.

2.Now we divide the first number with GCF as shown below



we get answer as 3.

3. Now to find LCM just multiply this answer to the other number!!!

So just watch how easily we get the LCM without writing all the multiples and finding the lowest of them.So the LCM of 24 and 64 is 192.

Now we will see how to apply this to three numbers:

Just take one more number, so we want to find the LCM of  24, 64 and 36

So first we find the LCM of 24 and 64 as shown we get it as 192. Now we do the LCM of 192 and 36 similarly. so we get the LCM of 24, 64, and 36 as shown below.


 
so we get the LCM of 24 , 64, and 36 as 576. Similarly we can do LCM of more numbers fast and easily.
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