PRACTICAL USE OF LCM

In this page practical use of lcm we are going to see real life application of taking L.C.M of any numbers.

Why we have to take L.C.M:

Consider the two number 15 and 12. Let us take L.C.M of those numbers.

  15 = 5 x 3

  12 = 2 x 2 x 3

L.C.M = 5 x 4 x 3

         = 60

Here l.c.m of 15 and 12 is 60. That is lease common multiple of 15 and 12 is 60. To verify this let us write 12 times table and 15 times table separately.

12 x 1 = 12         15 x 1 = 15

12 x 2 = 24         15 x 2 = 30 

12 x 3 = 36         15 x 3 = 45

12 x 4 = 48         15 x 4 = 60

12 x 5 = 60         15 x 5 = 75

12 x 6 = 72          15 x 6 = 90

12 x 7 = 84           15 x 7 =105

12 x 8 = 96           15 x 8 = 120

12 x 9 = 108

12 x 10 = 120

From this we come to know that in both tables we will get 60 and 120 so far  as common. In those values,least value is 60. This is what we are finding by taking L.C.M of two numbers without writing tables of those numbers.practical use of lcm practical use of lcm

To understand this topic much better let us consider the following example.

Example :

Two boys run on a circular track. They start at the same time. They take 12 minutes and 10 minutes respectively to go round once. Find at what time they will run together?

Solution:

Here two persons A and B are running in a circular track. They start at the same time and they are taking 12 minutes and 10 minutes respectively to go round once. From this details, we have to find that at what time they will run together. In other words, we can say that at what time they will meet each other.

Person A is taking 12 minutes to cover the circular track once. He is taking 24 minutes,36 minutes,48 minutes to cover the circular track 2 times,3 times and 4 times respectively.

Person B is taking 10 minutes to cover the circular track once. He is taking 20 minutes,30 minutes,40 minutes to cover the circular track 2 times,3 times and 4 times respectively.

12 x 1 = 12          10 x 1 = 10

12 x 2 = 24          10 x 2 = 20

12 x 3 = 36          10 x 3 = 30

12 x 4 = 48          10 x 4 = 40

12 x 5 = 60          10 x 5 = 50 

                           10 x 6 = 60

12 = 2 x 2 x 3

10 = 2 x 5

L.C.M = 4 x 5 x 3

         = 60  

From the above tables we get 60 as common. From this we can decide A and B would be together again after 60 minutes. In other words, we can say that they will meet each other after 60 minutes.