Question
Find Least Common Multiple of 300, 325 and 400 using prime factorisation method.
Answer
LCM( 300, 325, 400 ) = 15600
Explanation
Step 1: Write down factorisation of each number:
300 = 2 · 2 · 3 · 5 · 5
325 = 5 · 5 · 13
400 = 2 · 2 · 2 · 2 · 5 · 5
Step 2 : Match primes vertically:
| 300 | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | ||||||
| 325 | = | 5 | · | 5 | · | 13 | ||||||||||
| 400 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 300 | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | ||||||||
| 325 | = | 5 | · | 5 | · | 13 | ||||||||||||
| 400 | = | 2 | · | 2 | · | 2 | · | 2 | · | 5 | · | 5 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 13 | = | 15600 |
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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