Question
Find Least Common Multiple of 348, 756 and 396 using prime factorisation method.
Answer
LCM( 348, 756, 396 ) = 241164
Explanation
Step 1: Write down factorisation of each number:
348 = 2 · 2 · 3 · 29
756 = 2 · 2 · 3 · 3 · 3 · 7
396 = 2 · 2 · 3 · 3 · 11
Step 2 : Match primes vertically:
| 348 | = | 2 | · | 2 | · | 3 | · | 29 | ||||||||
| 756 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 7 | ||||
| 396 | = | 2 | · | 2 | · | 3 | · | 3 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 348 | = | 2 | · | 2 | · | 3 | · | 29 | ||||||||||
| 756 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 7 | ||||||
| 396 | = | 2 | · | 2 | · | 3 | · | 3 | · | 11 | ||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 7 | · | 11 | · | 29 | = | 241164 |
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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