Question
Find Least Common Multiple of 12, 268 and 44 using prime factorisation method.
Answer
LCM( 12, 268, 44 ) = 8844
Explanation
Step 1: Write down factorisation of each number:
12 = 2 · 2 · 3
268 = 2 · 2 · 67
44 = 2 · 2 · 11
Step 2 : Match primes vertically:
| 12 | = | 2 | · | 2 | · | 3 | ||||
| 268 | = | 2 | · | 2 | · | 67 | ||||
| 44 | = | 2 | · | 2 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 12 | = | 2 | · | 2 | · | 3 | ||||||
| 268 | = | 2 | · | 2 | · | 67 | ||||||
| 44 | = | 2 | · | 2 | · | 11 | ||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 11 | · | 67 | = | 8844 |
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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