Find Least Common Multiple of 224, 280 and 236 using prime factorisation method.
Answer
LCM( 224, 280, 236 ) = 66080
Explanation
Step 1: Write down factorisation of each number:
224 = 2 · 2 · 2 · 2 · 2 · 7
280 = 2 · 2 · 2 · 5 · 7
236 = 2 · 2 · 59
Step 2 : Match primes vertically:
| 224 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 7 | ||||
| 280 | = | 2 | · | 2 | · | 2 | · | 5 | · | 7 | ||||||
| 236 | = | 2 | · | 2 | · | 59 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 224 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 7 | ||||||
| 280 | = | 2 | · | 2 | · | 2 | · | 5 | · | 7 | ||||||||
| 236 | = | 2 | · | 2 | · | 59 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 7 | · | 59 | = | 66080 |
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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