LCM( 81, 135, 162 ) = 810
Step 1: Write down factorisation of each number:
81 = 3 · 3 · 3 · 3
135 = 3 · 3 · 3 · 5
162 = 2 · 3 · 3 · 3 · 3
Step 2 : Match primes vertically:
81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||
135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||
162 | = | 2 | · | 3 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||||
135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||||
162 | = | 2 | · | 3 | · | 3 | · | 3 | · | 3 | ||||
LCM | = | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 5 | = | 810 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.