Find Least Common Multiple of 31, 82 and 77 using prime factorisation method.
Answer
LCM( 31, 82, 77 ) = 195734
Explanation
Step 1: Write down factorisation of each number:
31 = 31
82 = 2 · 41
77 = 7 · 11
Step 2 : Match primes vertically:
| 31 | = | 31 | ||||||||
| 82 | = | 2 | · | 41 | ||||||
| 77 | = | 7 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 31 | = | 31 | ||||||||||
| 82 | = | 2 | · | 41 | ||||||||
| 77 | = | 7 | · | 11 | ||||||||
| LCM | = | 2 | · | 7 | · | 11 | · | 31 | · | 41 | = | 195734 |
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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