Find Least Common Multiple of 186, 246 and 280 using prime factorisation method.
Answer
LCM( 186, 246, 280 ) = 1067640
Explanation
Step 1: Write down factorisation of each number:
186 = 2 · 3 · 31
246 = 2 · 3 · 41
280 = 2 · 2 · 2 · 5 · 7
Step 2 : Match primes vertically:
| 186 | = | 2 | · | 3 | · | 31 | ||||||||||
| 246 | = | 2 | · | 3 | · | 41 | ||||||||||
| 280 | = | 2 | · | 2 | · | 2 | · | 5 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 186 | = | 2 | · | 3 | · | 31 | ||||||||||||
| 246 | = | 2 | · | 3 | · | 41 | ||||||||||||
| 280 | = | 2 | · | 2 | · | 2 | · | 5 | · | 7 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | · | 31 | · | 41 | = | 1067640 |
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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