Question
Find Least Common Multiple of 685, 192 and 189 using prime factorisation method.
Answer
LCM( 685, 192, 189 ) = 8285760
Explanation
Step 1: Write down factorisation of each number:
685 = 5 · 137
192 = 2 · 2 · 2 · 2 · 2 · 2 · 3
189 = 3 · 3 · 3 · 7
Step 2 : Match primes vertically:
| 685 | = | 5 | · | 137 | ||||||||||||||||||||
| 192 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||||||
| 189 | = | 3 | · | 3 | · | 3 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 685 | = | 5 | · | 137 | ||||||||||||||||||||||
| 192 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||||||||
| 189 | = | 3 | · | 3 | · | 3 | · | 7 | ||||||||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 7 | · | 137 | = | 8285760 |
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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