Question
Find Least Common Multiple of 800, 75 and 450 using prime factorisation method.
Answer
LCM( 800, 75, 450 ) = 7200
Explanation
Step 1: Write down factorisation of each number:
800 = 2 · 2 · 2 · 2 · 2 · 5 · 5
75 = 3 · 5 · 5
450 = 2 · 3 · 3 · 5 · 5
Step 2 : Match primes vertically:
| 800 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 5 | ||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||||||||
| 450 | = | 2 | · | 3 | · | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 800 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 5 | ||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||||||||||
| 450 | = | 2 | · | 3 | · | 3 | · | 5 | · | 5 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | = | 7200 |
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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