Page 75 - MathGPT_V1.0_C5

D:\Surender Prajapati\Books Final_CBSE and ICSE\ICSE\Preparatory_Stage_Maths-5_(31-10-2023)\Open_Files\CHAP_03
\\November 3, 2023 11:27 AM Surender Prajapati Proof 5 Reader _________________________ Date: ___________________74

Common Multiples Method

Example 1: Find the LCM of 24 and 32 using the common multiple method.
Solution:

Step 1: Write some multiples of number 24.
Multiples of 24 are 24, 48, 72, 96 , 120, 144, 168, 192, ...

Step 2: Write some multiples of number 32.
Multiples of 32 are 32, 64, 96 , 128, 160, 192, ...
Step 3: List the common multiples of both the numbers.

Common multiples of 24 and 32 are 96, 192, ...
Step 4: The smallest common multiple will be the required LCM.

Thus, the least common multiple (LCM) of 24 and 32 = 96
Prime Factorisation Method

Step 1: Express each given number as the product of its prime factors.
Step 2: Take each prime factor as many times as the highest number of times it appear in
the above prime factorisation.

Step 3: The product of all such prime factors is the required LCM.
Example 2: Find the LCM of 96 and 120.

Solution: We write the prime factorisation of each number. 2 96
96 = 2 × 2 × 2 × 2 × 2 × 3 2 48 2 120
2 60
120 = 2 × 2 × 2 × 3 × 5 2 24 2 30
Here, 2 appears maximum five times and 3 appears maximum 2 12 3 15
2
6
1 time and 5 appears maximum 1 time. 3 3 5 5
Thus, the LCM of 96 and 120 is 2 × 2 × 2 × 2 × 2 × 3 × 5 = 480 1 1

Division Method

To find the LCM of the given numbers by using division method, we follow the following
steps.

Step 1: Write the given numbers in a horizontal line, separating them by commas.
Step 2: Divide the numbers by smallest suitable prime numbers which exactly divides at
least two of the given numbers.
Step 3: Write the quotient directly below the numbers in the next row.

If any number is not divided by the choosen prime number, then bring it down in
the next row.
Step 4: Repeat the process of steps 2 and 3, till we get 1 as quotient for all the numbers.

Step 5: Multiply all the prime numbers by which you have divided the numbers.
The product obtained is the LCM of the given numbers.

Mathematics-5 73