Find Least Common Multiple of 75, 40 and 90 using prime factorisation method.
Answer
LCM( 75, 40, 90 ) = 1800
Explanation
Step 1: Write down factorisation of each number:
75 = 3 · 5 · 5
40 = 2 · 2 · 2 · 5
90 = 2 · 3 · 3 · 5
Step 2 : Match primes vertically:
| 75 | = | 3 | · | 5 | · | 5 | ||||||||
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||
| 90 | = | 2 | · | 3 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 75 | = | 3 | · | 5 | · | 5 | ||||||||||
| 40 | = | 2 | · | 2 | · | 2 | · | 5 | ||||||||
| 90 | = | 2 | · | 3 | · | 3 | · | 5 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | = | 1800 |
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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