Find Least Common Multiple of 72, 96 and 108 using prime factorisation method.
Answer
LCM( 72, 96, 108 ) = 864
Explanation
Step 1: Write down factorisation of each number:
72 = 2 · 2 · 2 · 3 · 3
96 = 2 · 2 · 2 · 2 · 2 · 3
108 = 2 · 2 · 3 · 3 · 3
Step 2 : Match primes vertically:
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
| 108 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 108 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | = | 864 |
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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