Find Least Common Multiple of 48, 64 and 130 using prime factorisation method.
Answer
LCM( 48, 64, 130 ) = 12480
Explanation
Step 1: Write down factorisation of each number:
48 = 2 · 2 · 2 · 2 · 3
64 = 2 · 2 · 2 · 2 · 2 · 2
130 = 2 · 5 · 13
Step 2 : Match primes vertically:
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 130 | = | 2 | · | 5 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 130 | = | 2 | · | 5 | · | 13 | ||||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 13 | = | 12480 |
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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