L.C.M of two numbers in 3 methods explained

Learn and know how to find L.C.M of two numbers in different methods. To find L.C.M, we have 3 methods that I will explain step by step.

L.C.M of two numbers in 3 methods explained

What is the meaning of L.C.M? L.C.M means L stands for Least or Lowest, C stands for Common and M stands for Multiple. As we are discussing about L.C.M of two numbers we say that the method of finding the least common multiple for the two numbers is called as L.C.M. Basically there are 3 methods for finding L.C.M

The 3 methods to find the L.C.M of numbers are

  • L-Division Method
  • Multiple Method
  • Prime Factorization Method

The above mentioned methods are used to find out L.C.M of numbers. So now we will discuss one by one with an example.

L.C.M of Numbers by L-Division Method:

This method is the regular and common method we use for finding L.C.M. First let us consider two numbers for finding L.C.M. So am taking 14 and 26 as two numbers.

L.C.M of two numbers in 3 methods explained

Observe the above picture clearly step by step is showing.

First draw “L” shape and write the numbers 14 and 26 and opposite to these numbers write 2 because both of these numbers are be divisible by 2.

In table of 2, 14 goes 7 times and 26 goes 13 times. So write 7 and 13 below 14 and 26.

Draw “L” shape and opposite to 7 and 13 write 7.

In table of 7, 7 goes 1 time and in table of 7, 13 won’t come so write 13 as it is.

Below 7 and 13, write 1 and 13 as shown in figure

Opposite to 1 and 13, write 13.

Carry down 1 as it is and in table of 13, 13 goes 1 time.

So write 1, 1 below 1, 13 as shown in figure.

Therefore the L.C.M of 14 and 26 is given as 2 x 7 x 13 = 182.

L.C.M of Numbers by Multiple Method:

In this method we need to write all the multiples of 14 and 26, then in that choose the least one. So the least multiple will be L.C.M of two numbers 14 and 26.

The Multiples of the number 14 are as follows: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210, 224, 238, 252, 266, 280, 294, 308, 322, 336, 350, 364,378…

The Multiples of the number 26 are follows: 26, 52, 78, 104, 130, 156, 182, 208, 234, 260, 286, 312, 338, 364, 390, 416, 442, 468, 494…

Common multiples of 14 and 26 are 182, 364…

The least common multiple in all the common multiples is 182.

So therefore, the L.C.M of two numbers 14 and 26 is 182.

L.C.M of two numbers by Prime Factorization Method:

First you have to know what is prime factorization? It means that writing the number as the product of prime factors. Now we will write 14 and 26 as the product of prime factors.

14 = 2 x 7

26 = 2 x 13

Now write each prime factor with highest power and multiply them, we get L.C.M. So we get 2 x 7 x 13 = 182. Therefore L.C.M of two numbers (14, 26) is 182.

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