Question

To find the LCM of two numbers. How to find LCM of two numbers?

Answer 1

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

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.

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.

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

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.