LCM of Two Numbers

When two numbers have the same numbers as their multiples, those multiples are said to be common multiples. The smallest number which is a common multiple of those two numbers is the LCM of two numbers. Let us explore the methods to find the LCM of two numbers.

The LCM of two numbers or the least common multiple of two numbers is the smallest number which is exactly divisible by two numbers and it is also a common multiple of those two numbers.
For example: Take any two numbers such as 23 and 46, let's find the LCM of these two numbers. Multiples of 23 = 23, 46, 69, 92, 115, 138 and so on. Multiples of 46 = 46, 92, 138, 184 and so on. Now take out the smallest common multiple of 23 and 46. We can see that the smallest common multiple is 46. So the LCM of 23 and 46 is 46. Therefore, 46 is the smallest common multiple or LCM of two numbers which is exactly divisible by both the numbers.

LCM of two numbers can be calculated by using four main methods. These four methods to find LCM are discussed below.

• Listing Multiples Method
• Prime Factorization Method
• Division Method
• HCF method

Finding LCM of Two Numbers by Listing Multiples Method

In the listing multiples method, we have to write down the multiples of two numbers up to the first common multiple. For example, find LCM of 5 and 9. Multiples of number 5 = 5, 10,15, 20, 25, 30, 35, 40, 45 and so on. Multiples of number 9 = 9, 18, 27, 36, 45 and so on. The first smallest common multiple is 45, of numbers 5 and 9. Hence the LCM of the two numbers is 45.

Finding LCM of Two Numbers by Prime Factorization Method

In this method, first, write down all the prime factors of two numbers then multiply each factor with the highest powers to calculate the LCM of two numbers. For example, find LCM of 18 and 24.
Prime factors of number 18 = 2 × 3²
Prime factors of number 24 = 2³ × 3
LCM of numbers 18 and 24 = 2³ × 3² = 72
Here we multiply all the prime factors that are 2 and 3 with the highest powers, to find the LCM of two numbers.

Finding LCM of two numbers by Division Method

To find LCM of two numbers by division method follow the following steps given below:

• Step 1: Write the two numbers in a horizontal line and separate the numbers by commas.
• Step 2: Divide the two numbers with prime numbers, if any number is not exactly divided write down the number in the next row.
• Step 3: Keep on dividing the two numbers by prime numbers, until not getting the results as 1 in the complete row.
• Step 4: LCM of two numbers is the product of all prime numbers obtained in a division method.

For example, let's find LCM of 6 and 15 by division method.

• Write the numbers 6 and 15 in a horizontal line and separate them by commas.
• Divide the 6 and 15 by prime numbers, if a number is not exactly divided write down in the next row.
• Divide the numbers 6 and 15 till not getting 1 in a complete row.
• LCM of 6 and 15 is the product of all prime numbers i.e. 2 × 3 × 5 = 30

Look at the image given below, which shows LCM of 6 and 15 by division method.

Finding LCM of two numbers by HCF method

Here we will use the relation between HCF and LCM to find the LCM of two numbers. The product of HCF of two numbers and the LCM of two numbers is equal to the product of two numbers. Therefore, the formula to find LCM of two numbers is, LCM of two numbers = product of two numbers ÷ HCF of two numbers.

Note: The LCM of two co-prime numbers is equal to the product of co-prime numbers because the highest common factor of prime numbers is 1.

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What is the LCM of Two Numbers? 

The LCM of two numbers is the number that is exactly divisible by those two numbers and also the smallest common multiple of both the numbers.

What are the Methods to Find LCM of Two Numbers?

LCM of two numbers can be found by four methods. They are,

• Listing Multiples Method
• Prime Factorization Method
• Division Method Method
• HCF Method 

How to Find the LCM of Two Numbers by Prime Factorization Method?

In this method we have to find the prime factors of two numbers after that we have to multiply all the factors with the highest powers. The resultant number is the LCM of two numbers.

What is the LCM of Two Co-Prime Numbers?  

The LCM of two co-prime numbers is the product of two numbers because the highest common factor is one.

What is the Relation Between HCF and LCM of Two Numbers?

The relation between HCF and LCM of two numbers can be explained as the product of HCF and LCM of two numbers is equal to the product of both the numbers.

What is the LCM of Two Numbers 5 and 7?

The LCM of two numbers 5 and 7 is 5 × 7 = 35. As the numbers are co-prime therefore the LCM of two numbers is equal to the product of numbers. 

How to Find LCM of Two Numbers By Division Method?

To find LCM of two numbers by division method follow the following steps given below:
Step 1: Make a table of columns and rows and write the two numbers in a horizontal line and put the commas between them. 
Step 2: Divide the two numbers with prime numbers. If the number is not exactly divided bring down the number in the next row.
Step 3: Continue dividing the two numbers by prime numbers, until not reach number 1 in a row.
Step 4: The answer will be the product of all prime numbers obtained by the division method.