Question
Find Least Common Multiple of 63, 105 and 426 using prime factorisation method.
Answer
LCM( 63, 105, 426 ) = 44730
Explanation
Step 1: Write down factorisation of each number:
63 = 3 · 3 · 7
105 = 3 · 5 · 7
426 = 2 · 3 · 71
Step 2 : Match primes vertically:
| 63 | = | 3 | · | 3 | · | 7 | ||||||
| 105 | = | 3 | · | 5 | · | 7 | ||||||
| 426 | = | 2 | · | 3 | · | 71 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 63 | = | 3 | · | 3 | · | 7 | ||||||||
| 105 | = | 3 | · | 5 | · | 7 | ||||||||
| 426 | = | 2 | · | 3 | · | 71 | ||||||||
| LCM | = | 2 | · | 3 | · | 3 | · | 5 | · | 7 | · | 71 | = | 44730 |
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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