Question
Find Least Common Multiple of 144, 7 and 96 using prime factorisation method.
Answer
LCM( 144, 7, 96 ) = 2016
Explanation
Step 1: Write down factorisation of each number:
144 = 2 · 2 · 2 · 2 · 3 · 3
7 = 7
96 = 2 · 2 · 2 · 2 · 2 · 3
Step 2 : Match primes vertically:
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||
| 7 | = | 7 | ||||||||||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 7 | = | 7 | ||||||||||||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 7 | = | 2016 |
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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