Find Least Common Multiple of 24, 36 and 54 using prime factorisation method.
Answer
LCM( 24, 36, 54 ) = 216
Explanation
Step 1: Write down factorisation of each number:
24 = 2 · 2 · 2 · 3
36 = 2 · 2 · 3 · 3
54 = 2 · 3 · 3 · 3
Step 2 : Match primes vertically:
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 24 | = | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | = | 216 |
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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