Find Least Common Multiple of 30, 96 and 150 using prime factorisation method.
Answer
LCM( 30, 96, 150 ) = 2400
Explanation
Step 1: Write down factorisation of each number:
30 = 2 · 3 · 5
96 = 2 · 2 · 2 · 2 · 2 · 3
150 = 2 · 3 · 5 · 5
Step 2 : Match primes vertically:
| 30 | = | 2 | · | 3 | · | 5 | ||||||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
| 150 | = | 2 | · | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 30 | = | 2 | · | 3 | · | 5 | ||||||||||||
| 96 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 150 | = | 2 | · | 3 | · | 5 | · | 5 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | = | 2400 |
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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