Calculation for LCM

LCM can be calculated using two methods. These are Prime Factorization Method and Division method. These two methods are discussed below:

LCM by Prime Factorisation Method

As the name suggests, in this method we first find the prime factors of the given numbers and using the prime factors of the given numbers we find the LCM. Let’s understand it with the help of an example.

Example: Find the LCM 16 and 72 using prime factorisation method.

Solution:

Step 1: find the prime factors of all the given numbers. 16 = 2 x 2 x 2 x 2 72 = 2 x 2 x 2 x 3 x 3

Step 2: Check the count of different factors of the given values. 2 : Four times in (16) 2 : three times in (72) 3 : two times in (72)

Step 3: Now the common factor based on the higher count will be taken and the rest will be ignored. 2: Four times (16) > 2: three times (72) higher count will taken. 3 is only present in the (72) hence it will be taken.

Step 4: Multiply the selected values to get the final answer LCM ( 16, 72) = 2 x 2 x 2 x 2 x 3 x 3 = 144.

LCM by Division Method

We can find LCM of two numbers using the division method. In this method we divide the given numbers by their common factors and then successively divide the quotient to get another quotient. This process continues till we get the quotient such that they are not divisible by any common number. Let’s understand this with the help of an example

Example: Find the LCM of 24 and 30 by Division Method.

Solution:

Step 1: Start by listing the numbers for which you want to find the LCM. For this we have 24 and 30.

Step 2: Identify the smallest prime number that can evenly divide both 24 and 30. In this case, it’s 2. Write down 2 on the left.

Step 3: Divide both 24 and 30 by 2. Write the quotients below the numbers. For 24 ÷ 2, the quotient is 12, and for 30 ÷ 2, the quotient is 15.

Step 4: Keep looking for common prime factors. If there are more, repeat the process. For 12 and 15, the common factor is 3. Write down 3 on the left.

Step 5: Divide 12 and 15 by 3. Write the quotients below the numbers. For 12 ÷ 3, the quotient is 4, and for 15 ÷ 3, the quotient is 5.

Step 6: Once there are no more common prime factors, the numbers inside the green box are the prime factors of the LCM. To calculate the LCM, multiply all these numbers together.

Step 7: So, LCM of 24 and 30 = 2 × 3 × 4 × 5 = 120.

HCF (Highest Common Factor) and LCM (Least Common Multiple) are fundamental concepts in mathematics, particularly in number theory. HCF is the highest common number which can exactly divide the two given numbers. LCM or Lowest Common Multiple is the common number that is divisible by both the given numbers. These concepts are essential tools for solving a wide range of mathematical problems.

In this article, we will learn about the definitions of HCF and LCM, their properties, and methods for calculating HCF and LCM. Along with this, all the possible varieties of HCF and LCM Questions have been discussed with solutions, and practice questions are provided on HCF and LCM for learners.