Find Least Common Multiple of 230, 184 and 267 using prime factorisation method.
Answer
LCM( 230, 184, 267 ) = 245640
Explanation
Step 1: Write down factorisation of each number:
230 = 2 · 5 · 23
184 = 2 · 2 · 2 · 23
267 = 3 · 89
Step 2 : Match primes vertically:
| 230 | = | 2 | · | 5 | · | 23 | ||||||||
| 184 | = | 2 | · | 2 | · | 2 | · | 23 | ||||||
| 267 | = | 3 | · | 89 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 230 | = | 2 | · | 5 | · | 23 | ||||||||||
| 184 | = | 2 | · | 2 | · | 2 | · | 23 | ||||||||
| 267 | = | 3 | · | 89 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 23 | · | 89 | = | 245640 |
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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