Question
Find Least Common Multiple of 49, 61 and 82 using prime factorisation method.
Answer
LCM( 49, 61, 82 ) = 245098
Explanation
Step 1: Write down factorisation of each number:
49 = 7 · 7
61 = 61
82 = 2 · 41
Step 2 : Match primes vertically:
| 49 | = | 7 | · | 7 | ||||||
| 61 | = | 61 | ||||||||
| 82 | = | 2 | · | 41 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 49 | = | 7 | · | 7 | ||||||||
| 61 | = | 61 | ||||||||||
| 82 | = | 2 | · | 41 | ||||||||
| LCM | = | 2 | · | 7 | · | 7 | · | 41 | · | 61 | = | 245098 |
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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