LCM( 60, 72, 96 ) = 1440
Step 1: Write down factorisation of each number:
60 = 2 · 2 · 3 · 5
72 = 2 · 2 · 2 · 3 · 3
96 = 2 · 2 · 2 · 2 · 2 · 3
Step 2 : Match primes vertically:
60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||
72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||||
72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||||
96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 1440 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.