Find Least Common Multiple of 405 and 455 using prime factorisation method.
Answer
LCM( 405, 455 ) = 36855
Explanation
Step 1: Write down factorisation of each number:
405 = 3 · 3 · 3 · 3 · 5
455 = 5 · 7 · 13
Step 2 : Match primes vertically:
| 405 | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | ||||
| 455 | = | 5 | · | 7 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 405 | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | ||||||
| 455 | = | 5 | · | 7 | · | 13 | ||||||||||
| LCM | = | 3 | · | 3 | · | 3 | · | 3 | · | 5 | · | 7 | · | 13 | = | 36855 |
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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