Question
Find Least Common Multiple of 360, 180 and 450 using prime factorisation method.
Answer
LCM( 360, 180, 450 ) = 1800
Explanation
Step 1: Write down factorisation of each number:
360 = 2 · 2 · 2 · 3 · 3 · 5
180 = 2 · 2 · 3 · 3 · 5
450 = 2 · 3 · 3 · 5 · 5
Step 2 : Match primes vertically:
| 360 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | ||
| 180 | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | ||||
| 450 | = | 2 | · | 3 | · | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 360 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | ||||
| 180 | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | ||||||
| 450 | = | 2 | · | 3 | · | 3 | · | 5 | · | 5 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | = | 1800 |
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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