Question
Find Least Common Multiple of 102, 68 and 136 using prime factorisation method.
Answer
LCM( 102, 68, 136 ) = 408
Explanation
Step 1: Write down factorisation of each number:
102 = 2 · 3 · 17
68 = 2 · 2 · 17
136 = 2 · 2 · 2 · 17
Step 2 : Match primes vertically:
| 102 | = | 2 | · | 3 | · | 17 | ||||
| 68 | = | 2 | · | 2 | · | 17 | ||||
| 136 | = | 2 | · | 2 | · | 2 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 102 | = | 2 | · | 3 | · | 17 | ||||||
| 68 | = | 2 | · | 2 | · | 17 | ||||||
| 136 | = | 2 | · | 2 | · | 2 | · | 17 | ||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 17 | = | 408 |
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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