Find Least Common Multiple of 36, 55 and 75 using prime factorisation method.
Answer
LCM( 36, 55, 75 ) = 9900
Explanation
Step 1: Write down factorisation of each number:
36 = 2 · 2 · 3 · 3
55 = 5 · 11
75 = 3 · 5 · 5
Step 2 : Match primes vertically:
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 55 | = | 5 | · | 11 | ||||||||||
| 75 | = | 3 | · | 5 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 36 | = | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| 55 | = | 5 | · | 11 | ||||||||||||
| 75 | = | 3 | · | 5 | · | 5 | ||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 11 | = | 9900 |
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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