How to Find LCM?

As we have already discussed, the least common multiple is the smallest common multiple for any two or more given numbers.

A multiple is a value we get when we multiply a number with another number. Like 4 is a multiple of 2, as we multiply 2 with 2, we get 4. Similarly, in the case of the maths table, you can see the multiples of a number when we multiply them from 1, 2, 3, 4, 5, 6 and so on but not with zero.

LCM Formula

Let a and b are two given integers. The formula to find the LCM of a & b is given by:

LCM (a,b) = (a x b)/GCD(a,b)

Where GCD (a,b) means Greatest Common Divisor or Highest Common Factor of a & b.

LCM Formula for Fractions

The formula to find the LCM of fractions is given by:

L.C.M. = L.C.M Of Numerator/H.C.F Of Denominator

Different Methods of LCM

There are three important methods by which we can find the LCM of two or more numbers. They are:

• Listing the Multiples
• Prime Factorisation Method
• Division Method

Listing the Multiples

The method to find the least common multiple of any given numbers is first to list down the multiples of specific numbers and then find the first common multiple between them. 

Suppose there are two numbers 11 and 33. Then by listing the multiples of 11 and 33, we get;

Multiples of 11 = 11, 22, 33, 44, 55, ….

Multiples of 33 = 33, 66, 99, ….

We can see, the first common multiple or the least common multiple of both the numbers is 33. Hence, the LCM (11, 33) = 33.

LCM By Prime Factorisation

Another method to find the LCM of the given numbers is prime factorization. Suppose, there are three numbers 12, 16 and 24. Let us write the prime factors of all three numbers individually.

12 = 2 x 2 x 3

16 = 2 x 2 x 2 x 2

24 = 2 x 2 x 2 x 3

Now writing the prime factors of all the three numbers together, we get;

12 x 16 x 24 = 2 x 2 x 3 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3

Now pairing the common prime factors we get the LCM. Hence, there are four 2’s and one 3. So the LCM of 12, 16 and 24 will be;

LCM (12, 16, 24) = 2 x 2 x 2 x 2 x 3 = 48

LCM By Division Method

Finding LCM of two numbers by division method is an easy method. Below are the steps to find the LCM by division method:

• First, write the numbers, separated by commas
• Now divide the numbers, by the smallest prime number. 
• If any number is not divisible, then write down that number and proceed further
• Keep on dividing the row of numbers by prime numbers, unless we get the results as 1 in the complete row
• Now LCM of the numbers will be equal to the product of all the prime numbers we obtained in the division method

Example: Find LCM of 10, 18 and 20 by division method.

Solution: Let us draw a table to divide the numbers by prime factors.

Prime factors	1st number	2nd number	3rd number
2	10	18	20
2	5	9	10
3	5	9	5
3	5	3	5
5	5	1	5
	1	1	1

Therefore, LCM (10, 18, 20) = 2 x 2 x 3 x 3 x 5 = 180

LCM of Two Numbers

Let us write multiples of 4 and 6 first,

4 : 4,8,12,16,20,24,28,…..

6: 6,12,18,24,30,36,42…..

From the above two expressions you can see, 4 and 6 have common multiples as 12 and 24. They may have more common multiple if we go beyond. Now, the smallest or least common multiple for 4 and 6 is 12. Therefore, 12 is the LCM of 4 and 6. Also, learn to find LCM of two numbers here.

LCM Table

Numbers	LCM
24 and 36	72
10 and 15	30
8 and 10	40
15 and 20	60