Find Least Common Multiple of 216, 314 and 520 using prime factorisation method.
Answer
LCM( 216, 314, 520 ) = 2204280
Explanation
Step 1: Write down factorisation of each number:
216 = 2 · 2 · 2 · 3 · 3 · 3
314 = 2 · 157
520 = 2 · 2 · 2 · 5 · 13
Step 2 : Match primes vertically:
| 216 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||||
| 314 | = | 2 | · | 157 | ||||||||||||||
| 520 | = | 2 | · | 2 | · | 2 | · | 5 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 216 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||||||
| 314 | = | 2 | · | 157 | ||||||||||||||||
| 520 | = | 2 | · | 2 | · | 2 | · | 5 | · | 13 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 13 | · | 157 | = | 2204280 |
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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