Question
Find Least Common Multiple of 45, 578 and 400 using prime factorisation method.
Answer
LCM( 45, 578, 400 ) = 1040400
Explanation
Step 1: Write down factorisation of each number:
45 = 3 · 3 · 5
578 = 2 · 17 · 17
400 = 2 · 2 · 2 · 2 · 5 · 5
Step 2 : Match primes vertically:
| 45 | = | 3 | · | 3 | · | 5 | ||||||||||||||
| 578 | = | 2 | · | 17 | · | 17 | ||||||||||||||
| 400 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 45 | = | 3 | · | 3 | · | 5 | ||||||||||||||||
| 578 | = | 2 | · | 17 | · | 17 | ||||||||||||||||
| 400 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 5 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 17 | · | 17 | = | 1040400 |
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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