Question
Find Least Common Multiple of 30 and 46 using prime factorisation method.
Answer
LCM( 30, 46 ) = 690
Explanation
Step 1: Write down factorisation of each number:
30 = 2 · 3 · 5
46 = 2 · 23
Step 2 : Match primes vertically:
| 30 | = | 2 | · | 3 | · | 5 | ||
| 46 | = | 2 | · | 23 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 30 | = | 2 | · | 3 | · | 5 | ||||
| 46 | = | 2 | · | 23 | ||||||
| LCM | = | 2 | · | 3 | · | 5 | · | 23 | = | 690 |
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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