how to find lcm of two numbers

LCM of Two Numbers

When two numbers accept the same numbers as their multiples, those multiples are said to exist common multiples. The smallest number which is a common multiple of those ii numbers is the LCM of ii numbers. Let united states explore the methods to find the LCM of 2 numbers.

1.	What is LCM of Two Numbers?
2.	How To Discover LCM of Two Numbers?
3.	Solved Examples
4.	Do Question
5.	FAQs on LCM of 2 Numbers

What is LCM of 2 Numbers?

The LCM of two numbers or the to the lowest degree mutual multiple of two numbers is the smallest number which is exactly divisible by two numbers and information technology is besides a common multiple of those two numbers.
For example: Have whatever two numbers such as 23 and 46, let's observe the LCM of these ii numbers. Multiples of 23 = 23, 46, 69, 92, 115, 138 and and then on. Multiples of 46 = 46, 92, 138, 184 and so on. At present accept out the smallest mutual multiple of 23 and 46. Nosotros can encounter 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.

How to Find LCM of Two Numbers?

LCM of 2 numbers can be calculated by using four principal methods. These four methods to discover LCM are discussed below.

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

Finding LCM of Two Numbers by Listing Multiples Method

In the listing multiples method, nosotros have to write downwardly the multiples of two numbers up to the get-go common multiple. For instance, detect LCM of 5 and 9. Multiples of number 5 = v, 10,15, xx, 25, xxx, 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 2 Numbers by Prime Factorization Method

In this method, start, write downwardly all the prime factors of two numbers then multiply each factor with the highest powers to calculate the LCM of two numbers. For instance, find LCM of 18 and 24.
Prime number factors of number xviii = ii × 3²
Prime factors of number 24 = two³ × 3
LCM of numbers xviii and 24 = 2³ × 3² = 72
Here we multiply all the prime factors that are two and 3 with the highest powers, to find the LCM of ii numbers.

Finding LCM of 2 numbers by Sectionalization Method

To find LCM of ii numbers by sectionalisation method follow the following steps given below:

• Step 1: Write the ii numbers in a horizontal line and split up the numbers by commas.
• Step 2: Divide the ii numbers with prime numbers, if any number is not exactly divided write down the number in the next row.
• Step 3: Proceed on dividing the two numbers past prime numbers, until non getting the results equally 1 in the complete row.
• Step four: LCM of 2 numbers is the product of all prime numbers obtained in a division method.

For instance, let's find LCM of 6 and xv by partitioning method.

• Write the numbers vi and xv in a horizontal line and split them past commas.
• Divide the 6 and xv past prime numbers, if a number is not exactly divided write down in the adjacent row.
• Carve up the numbers half dozen and 15 till non getting one in a complete row.
• LCM of 6 and 15 is the production of all prime number numbers i.e. two × 3 × 5 = xxx

Look at the epitome given beneath, which shows LCM of vi and 15 by division method.

Finding LCM of ii numbers by HCF method

Here nosotros will utilize the relation betwixt HCF and LCM to discover 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 ii numbers is, LCM of two numbers = product of 2 numbers ÷ HCF of two numbers.

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

Related Articles on LCM of Two Numbers

Check out the interesting topics to learn more about the LCM of two numbers.

• LCM Reckoner for 4 Numbers
• LCM Calculator
• Least Common Multiple
• Multiples
• Least common multiple formula

1. Case i: Find the LCM of 2 numbers 120 and 150 by using prime factorization.
   Solution: Prime factors of number 120 = 2³ × 3 × 5;
   Prime factors of number 150 = two × 3 × vⁱⁱ
   Production of all the prime factors with highest powers = 2³ × iii × 5ⁱⁱ = 600
   So the LCM of two numbers (120, 150) is 600.

2. Instance ii: What is the LCM of ii numbers if the production of two numbers is 3276 and their HCF is 6?
   Solution: Given, the product of ii numbers = 3276 and the HCF of two numbers = 6. The relation between HCF and LCM is, HCF of two numbers × LCM of two numbers = product of two numbers
   six × LCM of two numbers = 3276
   Therefore, LCM of ii numbers = 3276 ÷ half dozen = 546

3. Example three: Find the LCM of 2 numbers 20 and 80 by using the division method.

   Solution: To find LCM of two numbers by division method follow the post-obit steps given below:

   • Step one: Write the two numbers, twenty and 80 in a horizontal line and put the commas betwixt them.
   • Step ii: Split up the two numbers twenty and eighty with prime numbers i.e. 2, iii, v.., if any number is non exactly divided, notation downwards the number in the next row.
   • Step 3: Continue the division until non getting the results as 1 in the complete row.
   • Pace 4: LCM of two numbers is the production of all prime numbers obtained in a division method.

   Wait at the epitome and read out loud the steps to conspicuously empathise the procedure.

   

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FAQs on LCM of Ii Numbers

What is the LCM of Two Numbers?

The LCM of two numbers is the number that is exactly divisible by those ii numbers and as well 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 number Factorization Method
• Segmentation Method Method
• HCF Method

How to Observe the LCM of 2 Numbers by Prime Factorization Method?

In this method we accept 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 ane.

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

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

What is the LCM of Two Numbers 5 and vii?

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

How to Detect LCM of Two Numbers By Division Method?

To find LCM of two numbers by sectionalization method follow the following steps given below:
Pace 1: Make a tabular array of columns and rows and write the two numbers in a horizontal line and put the commas between them.
Footstep ii: Split up the two numbers with prime number numbers. If the number is not exactly divided bring downwards the number in the next row.
Step 3: Keep dividing the 2 numbers by prime number numbers, until non reach number i in a row.
Step 4: The respond will be the product of all prime numbers obtained by the segmentation method.

Source: https://www.cuemath.com/numbers/lcm-of-two-numbers/#:~:text=Finding%20LCM%20of%20two%20numbers%20by%20HCF%20method&text=The%20product%20of%20HCF%20of,%C3%B7%20HCF%20of%20two%20numbers.

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