Find Least Common Multiple of 324, 540 and 810 using prime factorisation method.
Answer
LCM( 324, 540, 810 ) = 1620
Explanation
Step 1: Write down factorisation of each number:
324 = 2 · 2 · 3 · 3 · 3 · 3
540 = 2 · 2 · 3 · 3 · 3 · 5
810 = 2 · 3 · 3 · 3 · 3 · 5
Step 2 : Match primes vertically:
| 324 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | ||
| 540 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | ||
| 810 | = | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 324 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | ||||
| 540 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | ||||
| 810 | = | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 5 | ||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | · | 5 | = | 1620 |
This solution can be visualized using a Venn diagram.
The LCM is equal to the product of all the numbers on the diagram.
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