Find Least Common Multiple of 218, 516 and 312 using prime factorisation method.
Answer
LCM( 218, 516, 312 ) = 1462344
Explanation
Step 1: Write down factorisation of each number:
218 = 2 · 109
516 = 2 · 2 · 3 · 43
312 = 2 · 2 · 2 · 3 · 13
Step 2 : Match primes vertically:
| 218 | = | 2 | · | 109 | ||||||||||
| 516 | = | 2 | · | 2 | · | 3 | · | 43 | ||||||
| 312 | = | 2 | · | 2 | · | 2 | · | 3 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 218 | = | 2 | · | 109 | ||||||||||||
| 516 | = | 2 | · | 2 | · | 3 | · | 43 | ||||||||
| 312 | = | 2 | · | 2 | · | 2 | · | 3 | · | 13 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 13 | · | 43 | · | 109 | = | 1462344 |
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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