Question
Find Least Common Multiple of 46, 54 and 112 using prime factorisation method.
Answer
LCM( 46, 54, 112 ) = 69552
Explanation
Step 1: Write down factorisation of each number:
46 = 2 · 23
54 = 2 · 3 · 3 · 3
112 = 2 · 2 · 2 · 2 · 7
Step 2 : Match primes vertically:
| 46 | = | 2 | · | 23 | ||||||||||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||||||
| 112 | = | 2 | · | 2 | · | 2 | · | 2 | · | 7 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 46 | = | 2 | · | 23 | ||||||||||||||||
| 54 | = | 2 | · | 3 | · | 3 | · | 3 | ||||||||||||
| 112 | = | 2 | · | 2 | · | 2 | · | 2 | · | 7 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 7 | · | 23 | = | 69552 |
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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