Find Least Common Multiple of 28, 15 and 34 using prime factorisation method.
Answer
LCM( 28, 15, 34 ) = 7140
Explanation
Step 1: Write down factorisation of each number:
28 = 2 · 2 · 7
15 = 3 · 5
34 = 2 · 17
Step 2 : Match primes vertically:
| 28 | = | 2 | · | 2 | · | 7 | ||||||
| 15 | = | 3 | · | 5 | ||||||||
| 34 | = | 2 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 28 | = | 2 | · | 2 | · | 7 | ||||||||
| 15 | = | 3 | · | 5 | ||||||||||
| 34 | = | 2 | · | 17 | ||||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 7 | · | 17 | = | 7140 |
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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