Question
Find Least Common Multiple of 164, 284 and 360 using prime factorisation method.
Answer
LCM( 164, 284, 360 ) = 1047960
Explanation
Step 1: Write down factorisation of each number:
164 = 2 · 2 · 41
284 = 2 · 2 · 71
360 = 2 · 2 · 2 · 3 · 3 · 5
Step 2 : Match primes vertically:
| 164 | = | 2 | · | 2 | · | 41 | ||||||||||
| 284 | = | 2 | · | 2 | · | 71 | ||||||||||
| 360 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 164 | = | 2 | · | 2 | · | 41 | ||||||||||||
| 284 | = | 2 | · | 2 | · | 71 | ||||||||||||
| 360 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 41 | · | 71 | = | 1047960 |
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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