Find Least Common Multiple of 385, 618 and 912 using prime factorisation method.
Answer
LCM( 385, 618, 912 ) = 36165360
Explanation
Step 1: Write down factorisation of each number:
385 = 5 · 7 · 11
618 = 2 · 3 · 103
912 = 2 · 2 · 2 · 2 · 3 · 19
Step 2 : Match primes vertically:
| 385 | = | 5 | · | 7 | · | 11 | ||||||||||||||
| 618 | = | 2 | · | 3 | · | 103 | ||||||||||||||
| 912 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 19 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 385 | = | 5 | · | 7 | · | 11 | ||||||||||||||||
| 618 | = | 2 | · | 3 | · | 103 | ||||||||||||||||
| 912 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 19 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | · | 11 | · | 19 | · | 103 | = | 36165360 |
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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