The lowest common multiple of two or many provtopicIded integers is called the Lowest Common Multiple (LCM). Additionally, it is referred to as the least common multiple.

We may use any of the following techniques to determine the LCM of two or more integers.

1. Frequently used method of common multiples

2. Method of prime factorization

3. Method of division

Method 1: Finding LCM using the concept of common multiples.

E.g.1: Find the lowest common multiple of the numbers 10 and 12.

Multiple of 8 = Multiples of 10 are as follows:

10, 20, 30, 40, 50, 60, 70, 80,......

Multiple of 12 = 12, 24, 36, 48, 60, 72, 84, …

Comparing the multiples of 8 and 12, we see that the common multiple of 8, 12 is 60.

The lowest common multiple of 8 and 12 is 60

E.g.2: Find the lowest common multiple of the numbers 12, 15.

Multiples of 15 are as follows: 15, 30, 45, 60, 75, 90,.....

Multiples of 12 are as follows: 12, 24, 36, 48, 60, 72, 84,....

LCM(15, 12) = 60

Method 2: Finding LCM using the Prime factorization method.

Now, we will use the method of Prime Factorization LCM Method

Step 1: Find the multiplicative multiples of the number.

10 = 2 x 5

12 = 2 x 2 x 3

Trick:  Pick the number which is occurring at least once as a multiple along with common multiples between the two numbers.

10 = 2 x 5

12 = 2 x 2 x 3 = 4 x 3

LCM(10, 12)

= 4 x 5 x 3

= 4 x 5 x 3

= 60

Let us take another example.

ConstopicIder some other numbers 15,12.

Step 1: Find the multiplicative multiples of the number.

15 = 3 x 5

12 = 2 x 2 x 3

Step 2: Rewriting the above numbers:

15 = 3 x 5

12 = 2^2 x 3 or 3 x 4

Step: 3

LCM(15, 12)

= 22 x 3 x 5

= 4 x 3 x 5

= 60

Method 3: Finding LCM using the Division Method.

ConstopicIder the numbers 15,12. Let’s us find the LCM using the division method.

Calculation:

2 12 15

2 6 15

3 3 15

5 1 5

1 1

How to perform common division?

For obtaining lcm of the two numbers 12 and 15, we started out with the division of the two numbers with 12 and 15. We constopicIdered the least number that would be in the denominator and the given two numbers will be divtopicIded by this least number. The answer came out to be 6 and 15. Then again we carried out the division of the numbers 6 and 15 with the least number 2. The answer came out to be 3 and 15. The topicIdea is you have to keep divtopicIding the given numbers by the least number. If any number is not divisible by the least number such as 15 in our case, then bring down the non-divisible number. You will have to carry out this form of the division until the remainder comes out to be one.

Thus, we have the factors as 2, 2, 3, 5, 1. When you multiply all these factors, you will get the lcm.

Therefore we have 2 x 2 x 3 x 5 x 1 = 60 as the LCM.

60 is the LCM.