Question
Find Least Common Multiple of 204, 100 and 68 using prime factorisation method.
Answer
LCM( 204, 100, 68 ) = 5100
Explanation
Step 1: Write down factorisation of each number:
204 = 2 · 2 · 3 · 17
100 = 2 · 2 · 5 · 5
68 = 2 · 2 · 17
Step 2 : Match primes vertically:
| 204 | = | 2 | · | 2 | · | 3 | · | 17 | ||||
| 100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||
| 68 | = | 2 | · | 2 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 204 | = | 2 | · | 2 | · | 3 | · | 17 | ||||||
| 100 | = | 2 | · | 2 | · | 5 | · | 5 | ||||||
| 68 | = | 2 | · | 2 | · | 17 | ||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 17 | = | 5100 |
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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