Find Least Common Multiple of 219, 582 and 776 using prime factorisation method.
Answer
LCM( 219, 582, 776 ) = 169944
Explanation
Step 1: Write down factorisation of each number:
219 = 3 · 73
582 = 2 · 3 · 97
776 = 2 · 2 · 2 · 97
Step 2 : Match primes vertically:
| 219 | = | 3 | · | 73 | ||||||||
| 582 | = | 2 | · | 3 | · | 97 | ||||||
| 776 | = | 2 | · | 2 | · | 2 | · | 97 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 219 | = | 3 | · | 73 | ||||||||||
| 582 | = | 2 | · | 3 | · | 97 | ||||||||
| 776 | = | 2 | · | 2 | · | 2 | · | 97 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 73 | · | 97 | = | 169944 |
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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