Find Least Common Multiple of 5, 10 and 15 using prime factorisation method.
Answer
LCM( 5, 10, 15 ) = 30
Explanation
Step 1: Write down factorisation of each number:
5 = 5
10 = 2 · 5
15 = 3 · 5
Step 2 : Match primes vertically:
| 5 | = | 5 | ||||
| 10 | = | 2 | · | 5 | ||
| 15 | = | 3 | · | 5 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 5 | = | 5 | ||||||
| 10 | = | 2 | · | 5 | ||||
| 15 | = | 3 | · | 5 | ||||
| LCM | = | 2 | · | 3 | · | 5 | = | 30 |
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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