Question
Find Least Common Multiple of 224, 266 and 294 using prime factorisation method.
Answer
LCM( 224, 266, 294 ) = 89376
Explanation
Step 1: Write down factorisation of each number:
224 = 2 · 2 · 2 · 2 · 2 · 7
266 = 2 · 7 · 19
294 = 2 · 3 · 7 · 7
Step 2 : Match primes vertically:
| 224 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 7 | ||||||
| 266 | = | 2 | · | 7 | · | 19 | ||||||||||||
| 294 | = | 2 | · | 3 | · | 7 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 224 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 7 | ||||||||
| 266 | = | 2 | · | 7 | · | 19 | ||||||||||||||
| 294 | = | 2 | · | 3 | · | 7 | · | 7 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 7 | · | 7 | · | 19 | = | 89376 |
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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