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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 one 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.

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

Step 1: Write 15, 20, 25 and 45 in a row.
3 15, 20, 25, 45
Step 2: Choose the smallest suitable prime number, 5 5, 20, 25, 15
which divides 15 and 45 exactly. 2 1, 4, 5, 3

Step 3: Write the quotient below the numbers and the 2 1, 2, 5, 3
numbers which cannot divide by 3, bring it down 3 1, 1, 5, 3
to the next row as it is. 5 1, 1, 5, 1
Step 4: Next, the suitable prime number is 5; divide the 1, 1, 1, 1

numbers by 5.
Step 5: Continue dividing till you get 1 as quotient for all the numbers.

Thus, the LCM of 15, 20, 25 and 45 = 3 × 5 × 2 × 2 × 3 × 5 = 900.
example 4: Find the LCM of:

(a) 20, 60 and 90 (b) 24, 40 and 72

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