Find Least Common Multiple of 54, 56 and 84 using prime factorisation method.
Answer
LCM( 54, 56, 84 ) = 1512
Explanation
Step 1: Write down factorisation of each number:
54 = 2 · 3 · 3 · 3
56 = 2 · 2 · 2 · 7
84 = 2 · 2 · 3 · 7
Step 2 : Match primes vertically:
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||
| 56 | = | 2 | · | 2 | · | 2 | · | 7 | ||||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||||
| 56 | = | 2 | · | 2 | · | 2 | · | 7 | ||||||||
| 84 | = | 2 | · | 2 | · | 3 | · | 7 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 7 | = | 1512 |
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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