Find Least Common Multiple of 45, 81 and 270 using prime factorisation method.
Answer
LCM( 45, 81, 270 ) = 810
Explanation
Step 1: Write down factorisation of each number:
45 = 3 · 3 · 5
81 = 3 · 3 · 3 · 3
270 = 2 · 3 · 3 · 3 · 5
Step 2 : Match primes vertically:
| 45 | = | 3 | · | 3 | · | 5 | ||||||
| 81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||
| 270 | = | 2 | · | 3 | · | 3 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 45 | = | 3 | · | 3 | · | 5 | ||||||||
| 81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||||
| 270 | = | 2 | · | 3 | · | 3 | · | 3 | · | 5 | ||||
| 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.
This page was created using
LCM Calculator