LCM Calculator - LCM of two Numbers Calculator

Least common multiple of two numbers is the lowest possible number which is divisible by both the numbers. It can be calculated for two, three, four or many numbers. To understand the concept of Least Common Multiple we need to first know about multiple, Multiple are those numbers which you will get when you multiply any number or value whose multiple you need to determine with any integer value.

For example:

15x1 = 15

15x2 = 30

15x3 = 45

15x4 = 60 and so on.

Here you found 15, 30, 45, 60 are multiples of 15.

Next you need to know about the common multiple, for finding the common multiple of any numbers let say for any two numbers, we need to first find out multiple of first number and then for second number. After that we have to check those multiples which are common in both.

For Example:

Finding common multiple of 15 and 20

Here you see 60, 120 is a common multiple of 15 and 20. If 15 x 4 is equal to 60, 15x8 is equal to 120 and when 20x3 is equal to 60, 20x6 is equal to 120.

Now let’s back to our topic which is the least common multiple which says lowest possible number which is divisible by both the numbers. In the above example we get 60, 120 are common multiples of 15 and 20, so the least common multiple will be 60 which is the lowest possible number.

There are several methods through which you can find the LCM of any two, three or many number are:

1. Listing Method of LCM
2. Prime Factorization Method of LCM
3. Division Method of LCM

Division method is the most simple and easy to apply method to determine LCM of any given numbers.

How to Find the LCM of Two Numbers Calculation Step by Step

As we said there are several methods through which you determine the LCM of any two numbers. One of the most common methods is the Division Method. Here we find steps to calculate least common multiple (LCM) by using Division Method for two numbers

1. Firstly, you need to find the lowest possible number which can divide both or any one of two numbers.
2. Next you need to check the quotient for both division numbers whether they are factors or prime numbers. Write down the quotient below the number.

• If they are factors then divide that factor with the lowest possible prime number such that it is divisible by both or any one of the two numbers. Write down the quotient below the number. If the lowest possible number is divided by only one number, then write another dividend number as it is in the next column.
•  If they are prime numbers then no need to divide further.

1. Next, Repeat the step one and two until you get prime numbers in quotient for both numbers.
2. After that check the numbers of divisor and quotient and multiply them with each other.

Note: If you get any number which is repeating in divisor and quotient then take them in power of that number.

1. After you multiply quotient and divisor you will get the least common multiple for those two numbers.

Solved Example: What is the LCM of Two Numbers

Example:

Find out the LCM of 15 and 20 using Division Method

Solution:

You need to first find out the number which can divide both or any one of the 15 and 20.

So, in this case 3 is the number which can divide 15 and 20 both with 5 and 4 Quotients of each respective division.

Here you can see 5 is a prime number which cannot be further divided with any other number except with 1 and 5 itself. You no need to divide it further.

And next is 4 which is not a prime number it can be divided by 2 and 4 itself, you need to use the lowest possible number which here is 2 and divide the 4 by 2 you get 2 in the quotient. Write down the quotient below the dividend 4.

After that you see in both numbers you finally get are prime number in the last column, In this case you got 5 in the last column of 15, And 2 in the last column of 20. 

Next multiply the divisor and quotient in last column with each other which is:

3 x 5 x 2 x 2 = 60

So, the least common multiple of 15 and 20 is 60.

• The LCM is associative: LCM(a, b) = LCM(b, a)
• The LCM is commutative: LCM(a, b, c) = LCM(LCM(a, b), c) = LCM(a, LCM(b, c))
• The LCM is distributive: LCM(da, db, dc) = dLCM(a, b, c)
• The LCM is related to the greatest common factor (GCF): LCM(a,b) = a × b / GCF(a,b) and GCF(a,b) = a × b / LCM(a,b)

hcflcm.com is a tool that has different types of calculators for LCM, GCF, HCF, etc. under one roof making it simple for you to solve your problems.

1. What is the LCM of 12 and 18?

Least Common multiple for 12 and 18 is 36.

2. How to find the lcm of 3 numbers?

Want to attain more about it then proceed and explore it! Choose it from the below accessible links and get a good grip on the concept. The lcm of three numbers can be calculated using the calculator “LCM of two or more Numbers Calculator”.Take help for the math concept you are solving from hcflcm.com and clear your ambiguities.

3. What is the LCM for 12 and 15?

The Lowest common multiple or LCM for 12 and 15 is 60.