LCM( 60, 90, 80 ) = 720
Step 1: Write down factorisation of each number:
60 = 2 · 2 · 3 · 5
90 = 2 · 3 · 3 · 5
80 = 2 · 2 · 2 · 2 · 5
Step 2 : Match primes vertically:
60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||
90 | = | 2 | · | 3 | · | 3 | · | 5 | ||||||
80 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||
90 | = | 2 | · | 3 | · | 3 | · | 5 | ||||||||
80 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | ||||||
LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | = | 720 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.