Question
Find Least Common Multiple of 350, 600 and 575 using prime factorisation method.
Answer
LCM( 350, 600, 575 ) = 96600
Explanation
Step 1: Write down factorisation of each number:
350 = 2 · 5 · 5 · 7
600 = 2 · 2 · 2 · 3 · 5 · 5
575 = 5 · 5 · 23
Step 2 : Match primes vertically:
| 350 | = | 2 | · | 5 | · | 5 | · | 7 | ||||||||
| 600 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | ||||
| 575 | = | 5 | · | 5 | · | 23 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 350 | = | 2 | · | 5 | · | 5 | · | 7 | ||||||||||
| 600 | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | ||||||
| 575 | = | 5 | · | 5 | · | 23 | ||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 7 | · | 23 | = | 96600 |
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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