Question
Find Least Common Multiple of 34, 51 and 85 using prime factorisation method.
Answer
LCM( 34, 51, 85 ) = 510
Explanation
Step 1: Write down factorisation of each number:
34 = 2 · 17
51 = 3 · 17
85 = 5 · 17
Step 2 : Match primes vertically:
| 34 | = | 2 | · | 17 | ||||
| 51 | = | 3 | · | 17 | ||||
| 85 | = | 5 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 34 | = | 2 | · | 17 | ||||||
| 51 | = | 3 | · | 17 | ||||||
| 85 | = | 5 | · | 17 | ||||||
| LCM | = | 2 | · | 3 | · | 5 | · | 17 | = | 510 |
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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