LCM FULL FORM

What is the full form of LCM in Maths?

In Maths, LCM full form is Least Common Multiple. In arithmetic, the least common multiple or LCM of numbers, say a and b, is known as LCM (a,b). And LCM is the smallest or least positive integer this is divisible through each a and b.

As an example, recall integers 2 and 6.

Multiples of 2 are: 2,4,6,8,10,12,…

Multiples of 6 are: 6,12,18,24….

Therefore, common multiples of 2 and 6 are 6,12,18,24,…and so on. So their least common multiple is 6.

Solved Example

Find the LCM of 4 and 12?

Now let’s try to find the LCM of 4 and 12.

Multiples of 4 are: 4,8,12,16,20,24,28,32,36…

Multiples of 12 are: 12,24,36,48,60,72…

Therefore, common multiples of 4 and 12 are 12,24,36… and so on.

LCM Of Numbers

Suppose there are numbers 4 and 8 whose LCM we want to find.

Therefore observing the multiples of 4 and 8 ,we get

multiples of 4=4,8,12,16, 20,24…..

multiples of 8=8,16, 24, 32, 40, 48, 56, …

We observe that the least common multiple of numbers, 4 and 8, is 8.

LCM With The Aid Of Prime Factorization Method

To calculate the LCM of numbers 60 and 12.

One manner to discover the LCM of the given numbers is as follows:

First list the prime factors of numbers 60 and 12.

60 = 2 x 2 x 3 x 5

12 = 2 ×2 × 3

Observing the frequency of given prime factors ,we get

2: two times

3:one time

5: one time

Therefor the LCM of 60 and 12 = 2 × 2 x 3 × 5 = 60

LCM By Means Of Division Method

Step1:Write the given numbers in a horizontal line, separating them by commas.

Step 2: Divide them by a suitable prime number, which exactly divides at least two of the given numbers.

Step 3: We put the quotient directly under the numbers in the next row. If the number is not divided exactly, we bring it down in the next row.

Step 4: We continue the process of step 2 and step 3 until all prime numbers or 1 is left in the last row.

Step 5: We multiply all the prime numbers by which we have divided and the prime numbers left in the last row. This product is the least common multiple of the given numbers.

Example:

Determine the LCM of the numbers 2,4,6.

Ans: The calculation is given as follows:

LCM = 2 x 2 x 3=12.

Solved Example

Q.1: Find the LCM of 8 and 14.

Solution:

Step 1: First, write down each number as a product of prime numbers.

8 = 2 × 2 × 2 = 2³

14 = 2 × 7

Step 2: The product of the highest powers of all the prime factors.

Here are the main factors 2 and 7

The highest power of 2 here = 2³

The highest power of 7 is here = 7

So LCM = 2³ × 7 = 56