Find Least Common Multiple of 36, 48 and 96 using prime factorisation method.
Answer
LCM( 36, 48, 96 ) = 288
Explanation
Step 1: Write down factorisation of each number:
36 = 2 · 2 · 3 · 3
48 = 2 · 2 · 2 · 2 · 3
96 = 2 · 2 · 2 · 2 · 2 · 3
Step 2 : Match primes vertically:
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | = | 288 |
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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