Question
Find Least Common Multiple of 35, 67 and 89 using prime factorisation method.
Answer
LCM( 35, 67, 89 ) = 208705
Explanation
Step 1: Write down factorisation of each number:
35 = 5 · 7
67 = 67
89 = 89
Step 2 : Match primes vertically:
| 35 | = | 5 | · | 7 | ||||
| 67 | = | 67 | ||||||
| 89 | = | 89 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 35 | = | 5 | · | 7 | ||||||
| 67 | = | 67 | ||||||||
| 89 | = | 89 | ||||||||
| LCM | = | 5 | · | 7 | · | 67 | · | 89 | = | 208705 |
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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