Find Least Common Multiple of 11, 27 and 81 using prime factorisation method.
Answer
LCM( 11, 27, 81 ) = 891
Explanation
Step 1: Write down factorisation of each number:
11 = 11
27 = 3 · 3 · 3
81 = 3 · 3 · 3 · 3
Step 2 : Match primes vertically:
| 11 | = | 11 | ||||||||
| 27 | = | 3 | · | 3 | · | 3 | ||||
| 81 | = | 3 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 11 | = | 11 | ||||||||||
| 27 | = | 3 | · | 3 | · | 3 | ||||||
| 81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||
| LCM | = | 3 | · | 3 | · | 3 | · | 3 | · | 11 | = | 891 |
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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