Find Least Common Multiple of 240, 420 and 660 using prime factorisation method.
Answer
LCM( 240, 420, 660 ) = 18480
Explanation
Step 1: Write down factorisation of each number:
240 = 2 · 2 · 2 · 2 · 3 · 5
420 = 2 · 2 · 3 · 5 · 7
660 = 2 · 2 · 3 · 5 · 11
Step 2 : Match primes vertically:
| 240 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||
| 420 | = | 2 | · | 2 | · | 3 | · | 5 | · | 7 | ||||||
| 660 | = | 2 | · | 2 | · | 3 | · | 5 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 240 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | ||||||
| 420 | = | 2 | · | 2 | · | 3 | · | 5 | · | 7 | ||||||||
| 660 | = | 2 | · | 2 | · | 3 | · | 5 | · | 11 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 7 | · | 11 | = | 18480 |
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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