Question
Find Least Common Multiple of 12, 82 and 91 using prime factorisation method.
Answer
LCM( 12, 82, 91 ) = 44772
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
82 = 2 · 41
91 = 7 · 13
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||||
| 82 | = | 2 | · | 41 | ||||||||
| 91 | = | 7 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||||
| 82 | = | 2 | · | 41 | ||||||||||
| 91 | = | 7 | · | 13 | ||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 7 | · | 13 | · | 41 | = | 44772 |
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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