Find Least Common Multiple of 102, 106 and 116 using prime factorisation method.
Answer
LCM( 102, 106, 116 ) = 313548
Explanation
Step 1: Write down factorisation of each number:
102 = 2 · 3 · 17
106 = 2 · 53
116 = 2 · 2 · 29
Step 2 : Match primes vertically:
| 102 | = | 2 | · | 3 | · | 17 | ||||||
| 106 | = | 2 | · | 53 | ||||||||
| 116 | = | 2 | · | 2 | · | 29 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 102 | = | 2 | · | 3 | · | 17 | ||||||||
| 106 | = | 2 | · | 53 | ||||||||||
| 116 | = | 2 | · | 2 | · | 29 | ||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 17 | · | 29 | · | 53 | = | 313548 |
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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