Question
Find Least Common Multiple of 7, 21 and 81 using prime factorisation method.
Answer
LCM( 7, 21, 81 ) = 567
Explanation
Step 1: Write down factorisation of each number:
7 = 7
21 = 3 · 7
81 = 3 · 3 · 3 · 3
Step 2 : Match primes vertically:
| 7 | = | 7 | ||||||||
| 21 | = | 3 | · | 7 | ||||||
| 81 | = | 3 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 7 | = | 7 | ||||||||||
| 21 | = | 3 | · | 7 | ||||||||
| 81 | = | 3 | · | 3 | · | 3 | · | 3 | ||||
| LCM | = | 3 | · | 3 | · | 3 | · | 3 | · | 7 | = | 567 |
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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