Question
Find Least Common Multiple of 104, 78 and 260 using prime factorisation method.
Answer
LCM( 104, 78, 260 ) = 1560
Explanation
Step 1: Write down factorisation of each number:
104 = 2 · 2 · 2 · 13
78 = 2 · 3 · 13
260 = 2 · 2 · 5 · 13
Step 2 : Match primes vertically:
| 104 | = | 2 | · | 2 | · | 2 | · | 13 | ||||
| 78 | = | 2 | · | 3 | · | 13 | ||||||
| 260 | = | 2 | · | 2 | · | 5 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 104 | = | 2 | · | 2 | · | 2 | · | 13 | ||||||
| 78 | = | 2 | · | 3 | · | 13 | ||||||||
| 260 | = | 2 | · | 2 | · | 5 | · | 13 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 13 | = | 1560 |
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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