Find Least Common Multiple of 455, 117 and 338 using prime factorisation method.
Answer
LCM( 455, 117, 338 ) = 106470
Explanation
Step 1: Write down factorisation of each number:
455 = 5 · 7 · 13
117 = 3 · 3 · 13
338 = 2 · 13 · 13
Step 2 : Match primes vertically:
| 455 | = | 5 | · | 7 | · | 13 | ||||||||
| 117 | = | 3 | · | 3 | · | 13 | ||||||||
| 338 | = | 2 | · | 13 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 455 | = | 5 | · | 7 | · | 13 | ||||||||||
| 117 | = | 3 | · | 3 | · | 13 | ||||||||||
| 338 | = | 2 | · | 13 | · | 13 | ||||||||||
| LCM | = | 2 | · | 3 | · | 3 | · | 5 | · | 7 | · | 13 | · | 13 | = | 106470 |
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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