Find Least Common Multiple of 390, 660 and 900 using prime factorisation method.
Answer
LCM( 390, 660, 900 ) = 128700
Explanation
Step 1: Write down factorisation of each number:
390 = 2 · 3 · 5 · 13
660 = 2 · 2 · 3 · 5 · 11
900 = 2 · 2 · 3 · 3 · 5 · 5
Step 2 : Match primes vertically:
| 390 | = | 2 | · | 3 | · | 5 | · | 13 | ||||||||
| 660 | = | 2 | · | 2 | · | 3 | · | 5 | · | 11 | ||||||
| 900 | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 390 | = | 2 | · | 3 | · | 5 | · | 13 | ||||||||||
| 660 | = | 2 | · | 2 | · | 3 | · | 5 | · | 11 | ||||||||
| 900 | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | ||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 11 | · | 13 | = | 128700 |
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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