LCM calculator

Least Common Multiple Calculator

This Least Common multiple calculator is one of the best math tools one can find online. The user simply has to enter the values. It can find LCM by all of the three basic and commonly used methods.

In this LCM calculator, each of the methods is presented step-wise in the results for the user’s understanding. You can also see the GCF of the entered values under the LCM. 

What is LCM?

LCM stands for least common multiple. It is that one smallest value that can divide the two or more numbers. 

In other words, it is the first common number that comes in the multiple tables of the numbers under study. 

How to find the LCM?

LCM can be found by three main methods. These methods are;

• Prime factorization
• Division table
• List of multiples

The easy and better option to find LCM is by using the LCM finder on top. But for manual calculation, follow the example below.

Example:

What is lcm of 34, 20, and 10?

Prime factorization

Step 1: Write all of the Prime factors of the numbers.

34 = 2 x 17 

20 = 2 x 2 x 5 = 22 x 5

10 = 2 x 5

Step 2: Multiply the prime factors. (If there are common factors like in this case 2 and 5, use them only once.)

= 17 x 5 x 22 = 340

Hence the least common multiple of 34, 20, and 10 is 340. Now, let’s also find the LCM using the other two methods.

Division table

In this method, the numbers are written on a horizontal line. Then they are divided by the common (if any) and smallest prime number. And it goes on until no more division is possible.

Step 1: Write the numbers on the table.

Step 2: Divide the numbers as guided before. Write the quotients directly below the number.

Step 3: Multiply all of the divisors.

= 2 x 2 x 5 x 17 = 340

List of the multiples

The last way to find the lcm of two or more numbers is by listing down all of their multiples until they have at least one common factor. 

Step 1: Write the multiples. 

Multiples of 34: 34, 68, 102, 136, 170, 204, 238, 272, 306, 340, 374, 408.

Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380.

Multiples of 10: 10, 20 ,30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200, 210, 220, 230, 240, 250, 260, 270, 280, 290, 300, 310, 320, 330, 340, 350, 360.

Step 2: Look for the first common factor.

The first common factor of 34, 20, and 10 is 340. The LCM of these numbers is 340.

LCM Table

LCM of 6 and 8	24
LCM of 6 and 9	18
LCM of 6 and 12	12
LCM of 8 and 12	24
LCM of 9 and 12	36
LCM of 8 and 10	40
LCM of 4 and 6	12
LCM of 6 and 10	30
LCM of 4 and 10	20
LCM of 3 and 8	24
LCM of 3 and 5	15
LCM of 20 and 40	40
LCM of 12 and 15	60
LCM of 18 and 30	90
LCM of 5 and 8	40
lcm of 4, 9 and 12	36
lcm of 3, 5 and 6	30