Question
Find Least Common Multiple of 6, 675 and 9 using prime factorisation method.
Answer
LCM( 6, 675, 9 ) = 1350
Explanation
Step 1: Write down factorisation of each number:
6 = 2 · 3
675 = 3 · 3 · 3 · 5 · 5
9 = 3 · 3
Step 2 : Match primes vertically:
| 6 | = | 2 | · | 3 | ||||||||
| 675 | = | 3 | · | 3 | · | 3 | · | 5 | · | 5 | ||
| 9 | = | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 6 | = | 2 | · | 3 | ||||||||||
| 675 | = | 3 | · | 3 | · | 3 | · | 5 | · | 5 | ||||
| 9 | = | 3 | · | 3 | ||||||||||
| LCM | = | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 5 | = | 1350 |
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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