Find Least Common Multiple of 525, 425 and 343 using prime factorisation method.
Answer
LCM( 525, 425, 343 ) = 437325
Explanation
Step 1: Write down factorisation of each number:
525 = 3 · 5 · 5 · 7
425 = 5 · 5 · 17
343 = 7 · 7 · 7
Step 2 : Match primes vertically:
| 525 | = | 3 | · | 5 | · | 5 | · | 7 | ||||||
| 425 | = | 5 | · | 5 | · | 17 | ||||||||
| 343 | = | 7 | · | 7 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 525 | = | 3 | · | 5 | · | 5 | · | 7 | ||||||||
| 425 | = | 5 | · | 5 | · | 17 | ||||||||||
| 343 | = | 7 | · | 7 | · | 7 | ||||||||||
| LCM | = | 3 | · | 5 | · | 5 | · | 7 | · | 7 | · | 7 | · | 17 | = | 437325 |
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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