Least Common Multiple

The Least Common Multiple (LCM) is considered as the least or the lowest number that happens to be a multiple of two more numbers. The Least Common Factor (LCM) can be expressed as LCM(x, y). It is also termed as Lowest Common Multiple.

We will now learn the different ways of finding out the Least Common Factor (LCM).

There are three methods of solving the Least Common Multiple (LCM). They are listed below:

1. The Common Multiple Method.
2. The Prime Factor Method.
3. The Common Division Method.

We will study each method separately.

Common Multiple Method:

In this method, out of the list of the multiples, the least common multiple is first identified and it is considered as the LCM of the listed numbers.

How to find out LCM?

Step-1 First, we need to list down a few multiples of each of the numbers given.

Step-2 Then, we have to identify a common multiple out of the list of several multiples of the given numbers.

Step-3 Lastly, the least common multiple is required to be taken into account.

Problem:

What will be the LCM of the numbers 2,4, 6?

Solution:

Let us denote the numbers as X2, X4, and X6.

X2 = 2 = 2, 4, 6, 8, 10, 12, 14………

X4 = 4 = 4, 8, 12, 16, 20, 24, 28……..

X6 = 6 = 6, 12, 18, 24, 30, 36, 42……..

Now, we have to identify a common multiple out of the multiples listed above.

12 is the common multiple of 2, 4, and 6.

The LCM of 2,4,6 is 12.

Prime Factor Method:

In this particular method, we find the LCM by splitting the given numbers as prime factors.

How to find out LCM?

Steps to find out LCM are as follows:-

Step-1 First, we have to determine that each number is a product of the prime numbers.

Step-2 The Prime numbers are to be expressed in index form with the use of exponentiation.

Step-3 Finally, we will get the product of all the prime factors having the highest power in the given numbers.

Example:

Let’s take three different numbers, say, 8, 16, and 24. We will divide them as follows:

8 = 2 * 2* 2 = 23.

16= 2 * 2 * 2 * 2= 24.

24 = 2 * 2 * 2 * 3 = 23 * 31.

 The prime factors with the highest power are 24 and 31.

 Now, we will take out the LCM,

LCM= 24 * 31.

LCM= 16* 3= 48.

Common Division Method:

Step-1 We will have to draw two perpendicular intersecting lines.

Step-2 The numbers are to be separated by a comma on the vertical line. We will have to take a suitable number that divides at least two given numbers and note it down on the left side of the vertical line and which will lie above the horizontal line.

Step-3 A horizontal line has to be drawn and the vertical line needs to be extended if we find that at least two of the numbers from the quotients and the number being undivided is divisible by a number chosen.

Step-4 We will have to continue the process until we have the numbers in which at least two of the numbers will remain undivided by any other number.

The Least Common Multiple Calculator can be defined as a tool that is usually available online, required to calculate a least common factor of at least two or more than two numbers.

How to use the LCM calculator?

 The below-listed steps are to be followed for the proper operation of the calculator.

• Firstly, we have to enter the values given in the input box.
• Then we have to separate each of the given values with the help of a comma.
• After this, we have to press the button “ Calculate” to obtain the least common factors of the entered values.
• Finally, we will press the button labeled “ Reset” for a new calculation.

Conclusion:

Thus, it is very important to clear the fundamental concepts/basics of the Least Common Factor. It is applied in topics such as permutation and combinations, factorization, etc. They need a precise understanding which will help us solve the complex problems of Quant.