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Step 3: Multiply the common prime factors. The product of common
prime factors is the required HCF.

So, the HCF of 18 and 42 = 2 × 3 = 6.
Example 3: Find the HCF of 14, 28 and 70 by common division.
Solution: Step 1: Arrange the given numbers in a row as shown here. 14, 28, 70

Step 2: Choose a common prime divisor and divide all the numbers.
Write the quotients in the next row just below the numbers as
shown. 2 14, 28, 70

Here, the smallest common prime divisor is 2. 7, 14, 35
Step 3: Continue the step 2 till the numbers have any 2 14, 28, 70
common prime divisor as shown alongside. 7 7, 14, 35

Here, the next common prime divisor is 7. 1, 2, 5

Step 4: Multiply the common divisors. The
product of the common prime divisors Quick Check
is the required HCF. Find the hCF of:
Thus, HCF of 14, 28 and 70 = 2 × 7 = 14. 1. 10 and 15

lowest common Multiple (lcM)
2. 16 and 20
Let us consider the multiples of 3 and 4. 3. 18, 30 and 48

The multiples of 3 are: 3, 6, 9, 12, 15, 18, 21, 24, 27, …
The multiples of 4 are: 4, 8, 12, 16, 20, 24, 28, 32, 36, …

The common multiples of 3 and 4 are: 12, 24, 36, …
Here, we see the smallest common multiple is 12. So, 12 is called the LCM of 3 and 4.

Thus, the smallest number which is divisible by all the given numbers is called their
Least Common Multiple.
Finding lcM

We can find the LCM of given numbers using the following methods:

1. By listing common multiples 2. By prime factorisation

3. By common division
Let us understand these methods through examples.
Example 4: Find the LCM of 6 and 9 by listing multiples.

Solution: Step 1: List some multiples of all the given numbers.

The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …
The multiples of 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …

Step 2: Choose the common multiples.
The common multiples of 6 and 9 are: 18, 36, 54, ...

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