Question
Find Least Common Multiple of 12, 18 and 81 using prime factorisation method.
Answer
LCM( 12, 18, 81 ) = 324
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
18 = 2 · 3 · 3
81 = 3 · 3 · 3 · 3
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||
| 81 | = | 3 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 18 | = | 2 | · | 3 | · | 3 | ||||||||
| 81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 3 | = | 324 |
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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