Find Least Common Multiple of 105, 45 and 75 using prime factorisation method.
Answer
LCM( 105, 45, 75 ) = 1575
Explanation
Step 1: Write down factorisation of each number:
105 = 3 · 5 · 7
45 = 3 · 3 · 5
75 = 3 · 5 · 5
Step 2 : Match primes vertically:
| 105 | = | 3 | · | 5 | · | 7 | ||||
| 45 | = | 3 | · | 3 | · | 5 | ||||
| 75 | = | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 105 | = | 3 | · | 5 | · | 7 | ||||||
| 45 | = | 3 | · | 3 | · | 5 | ||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||
| LCM | = | 3 | · | 3 | · | 5 | · | 5 | · | 7 | = | 1575 |
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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