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\\October 8, 2025 12:13 PM Bharat Arora P-9 Reader _________________________ Date: ___________________74

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 factorisations.

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 2 120
96 = 2 × 2 × 2 × 2 × 2 × 3 2 48 2 60

120 = 2 × 2 × 2 × 3 × 5 2 24 2 30
2 12
Here, 2 appears a maximum of five times and 3 appears 2 6 3 15
maximum 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 using the division method, we follow the steps.
Step 1: Write the given numbers in a horizontal line, separating them by commas.

Step 2: Divide the numbers by the smallest suitable prime number which exactly divides at
least one of the given numbers.

Step 3: Write the quotient directly below the numbers in the next row.
If any number is not divisible by the chosen prime number, then bring it down in
the next row.
Step 4: Repeat steps 2 and 3, till we get 1 as the 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.

example 3: Find the LCM of 15, 20, 25 and 45 using the division method.

Solution: We have 15, 20, 25 and 45. 3 15, 20, 25, 45
Step 1: Write 15, 20, 25 and 45 in a row. 5 5, 20, 25, 15

Step 2: Choose the smallest suitable prime number 2 1, 4, 5, 3
which divides 15 and 45 exactly. 2 1, 2, 5, 3
Step 3: Write the quotients below the numbers. Those 3 1, 1, 5, 3
numbers that are not divisible by 3 can be 5 1, 1, 5, 1
written in the next row as they are. 1, 1, 1, 1

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