Find Least Common Multiple of 45, 34 and 67 using prime factorisation method.
Answer
LCM( 45, 34, 67 ) = 102510
Explanation
Step 1: Write down factorisation of each number:
45 = 3 · 3 · 5
34 = 2 · 17
67 = 67
Step 2 : Match primes vertically:
| 45 | = | 3 | · | 3 | · | 5 | ||||||
| 34 | = | 2 | · | 17 | ||||||||
| 67 | = | 67 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 45 | = | 3 | · | 3 | · | 5 | ||||||||
| 34 | = | 2 | · | 17 | ||||||||||
| 67 | = | 67 | ||||||||||||
| LCM | = | 2 | · | 3 | · | 3 | · | 5 | · | 17 | · | 67 | = | 102510 |
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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