LCM -Least Common Multiple





LCM of two or more non zero whole numbers is the smallest whole number which is a multiple of each given number. In other words it must be the smallest whole number which is divisible by each number.

Method 1:

In this method we have to first list multiples of each of the given number, and we have to find out the smallest one which is a common number in each list.

Examples:

Find the least common multiple(LCM) of 5, 6 and 15.

Solution:

First we list the multiples of each number.

    1. Multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60,...
    2. Multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48,54,60,...
    3. Multiples of 15 are: 15, 30, 45, 60,....
  • Listing the common multiples; 30, 60,...
  • Least common multiple(LCM) is 30.

Method 2:

In this method,

  1. we have to factor the given numbers, into its prime factors.
  2. we have to count the number of times each prime factor appear for each given number. We have to consider the largest number of times of factors.
  3. We have to write the remaining prime factors, which are appearing once for each given numbers.
  4. Now we have to multiply all the prime factors written.

Example 1 :

Find the LCM of 27, 84 and 90.

Solution:

  1. Factors of 27: 3 3 3

    Factors of 84: 2 2 3 7.

    Factors of 90: 2 3 3 5

  2. Here 3 appears 3 times, 2 appears 2 times and 5 and 7 appear one time each
  3. L.C.M = 2x2x3x3x3x5x7 = 3,780


Example 2 :

Find the L.C.M of x3 + 1,x2 - 1,(x+1)2.

Solution:

  1. x3 + 1 = (x+1)(x2 - x + 1)

    x2 - 1 = (x+1) (x-1)

    (x+1)2 = (x+1)(x+1)

  2. L.C.M = (x+1)2(x+1) (x2 - x + 1)




Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life. They are:

It subtracts sadness and adds happiness in our life.

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”






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