LCM( 144, 7, 96 ) = 2016
Step 1: Write down factorisation of each number:
144 = 2 · 2 · 2 · 2 · 3 · 3
7 = 7
96 = 2 · 2 · 2 · 2 · 2 · 3
Step 2 : Match primes vertically:
144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||
7 | = | 7 | ||||||||||||||
96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
7 | = | 7 | ||||||||||||||||
96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | = | 2016 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.