1. LCM
The lowest common multiple or least common multiple (LCM) is the smallest number that belongs to the multiplication table of two or more numbers.
Lowest means smallest number
Common means shared between two or more numbers
Multiple is a number that can be divided by the given number without leaving a reminder
So basically, multiples that are shared by two or more whole numbers are called common multiples. The smallest common multiples are called the least common multiple (LCM).
Let's learn the different methods to find the LCM of numbers
2. How to find LCM:
The different methods to find the least common multiple of two or more numbers are:
- By listing multiples
- Using prime factorisation
2.1 By Listing Multiples
This is commonly used to find the LCM by listing multiples of given numbers. From available multiples, we have to select a common multiple and it should be the least. By doing this we will get LCM of those two numbers.
Example: Find the lowest common multiple (LCM) of 2 and 5.
Step 01: Write down the multiples of 2 and 5
Multiples of 2 : 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32,…
Multiples of 5 : 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, …
Step 02: Write down the common multiples of 2 and 5
Common multiples of 2 and 5 are 10, 20, 30 …….
Step 03: Select the lowest number from the common multiples list
So the lowest common multiple of 2 and 5 is 10.
Example: Find the lowest common multiple (LCM) of 3 and 8.
Step 01: Write down the multiples of 3 and 8
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, ……
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, ……
Step 02: Write down the common multiples of 3 and 8
Common multiples of 3 and 8 are 24, 48,…….
Step 03: Select the lowest number from the common multiples list
So the lowest common multiple of 3 and 8 is 24.
2.2 Using the Prime Factorisation
In this method, first do the prime factorisation of given numbers. Then multiply all the prime factors that appear in either number. By doing this, we will get the LCM of the given numbers.
Example:1 Find the lowest common multiple (LCM) of 8 and 12.
Step 01: Do the prime factorisations of 8 and 12
Prime factorisation of 8 = 2 x 2 x 2
Prime factorisation of 12 = 2 x 2 x 3
Step 02: Write down all the factors of 8 and 12 that appear in either number
The factors are: 2, 2, 2 and 3.
To find the LCM multiply these numbers. So LCM = 2 x 2 x 2 x 3 = 24
