Find Least Common Multiple of 96, 64 and 27 using prime factorisation method.
Answer
LCM( 96, 64, 27 ) = 1728
Explanation
Step 1: Write down factorisation of each number:
96 = 2 · 2 · 2 · 2 · 2 · 3
64 = 2 · 2 · 2 · 2 · 2 · 2
27 = 3 · 3 · 3
Step 2 : Match primes vertically:
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||
| 27 | = | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||||
| 64 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | ||||||||
| 27 | = | 3 | · | 3 | · | 3 | ||||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | = | 1728 |
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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