LCM( 27, 54, 135 ) = 270
Step 1: Write down factorisation of each number:
27 = 3 · 3 · 3
54 = 2 · 3 · 3 · 3
135 = 3 · 3 · 3 · 5
Step 2 : Match primes vertically:
27 | = | 3 | · | 3 | · | 3 | ||||
54 | = | 2 | · | 3 | · | 3 | · | 3 | ||
135 | = | 3 | · | 3 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
27 | = | 3 | · | 3 | · | 3 | ||||||
54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||
135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||
LCM | = | 2 | · | 3 | · | 3 | · | 3 | · | 5 | = | 270 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.