Find Least Common Multiple of 135, 126 and 255 using prime factorisation method.
Answer
LCM( 135, 126, 255 ) = 32130
Explanation
Step 1: Write down factorisation of each number:
135 = 3 · 3 · 3 · 5
126 = 2 · 3 · 3 · 7
255 = 3 · 5 · 17
Step 2 : Match primes vertically:
| 135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||||
| 126 | = | 2 | · | 3 | · | 3 | · | 7 | ||||||
| 255 | = | 3 | · | 5 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 135 | = | 3 | · | 3 | · | 3 | · | 5 | ||||||||
| 126 | = | 2 | · | 3 | · | 3 | · | 7 | ||||||||
| 255 | = | 3 | · | 5 | · | 17 | ||||||||||
| LCM | = | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 7 | · | 17 | = | 32130 |
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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