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The lowest common multiple (LCM) of two or more given numbers is the lowest (or smallest or
least) of their common multiples.

Remember

The Lowest/least common multiple of two or more numbers is the smallest number which is divisible by each
of the given numbers.

Finding LCM

Just like HCF, LCM of two or more numbers can be found by using any one of three methods.
1. Common multiples method 2. Prime factorisation method 3. Division method
Common Multiples Method

Follow these steps to find the LCM of two or more numbers by common multiples method.
Step 1: Write down some multiples of the given numbers.
Step 2: Find out the common multiples from the list.

Step 3: Write the smallest common multiple as the LCM of the given numbers.
Example 25: Find the LCM of 12 and 18.

Solution: We know that:
Multiples of 12 are 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ...
Multiples of 18 are 18, 36, 54, 72, 90, 108, 126, 144, 162, ...

Common multiples of 12 and 18 are 36, 72, 108, …
The lowest of these is 36. So, the LCM of 12 and 18 is 36.

Prime Factorisation Method

Follow these steps to find the LCM of two or more numbers by prime factorisation method.
Step 1: Express each number as a product of its prime factors.

Step 2: Look for the maximum number of times each factor appears in any factorisation.
Step 3: Find the product of prime factors. This is the LCM of given numbers.
Example 26: Find the LCM of 20, 25 and 30.

Solution: By getting prime factorisation of these numbers,

2 20 5 25 2 30

2 10 5 3 15

5 5

20 = 2 × 2 × 5 25 = 5 × 5 30 = 2 × 3 × 5

In these prime factorisations, the maximum number of times the prime factor 2 occurs is two; this
happens for 20. Similarly, the maximum number of times the factor 3 occurs is one; this happens
for 30, and the factor 5 occurs is two; this happens for 25.

So, the LCM of 20, 25 and 30 = 2 × 2 × 3 × 5 × 5 = 300.

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