Question
Find Least Common Multiple of 92, 104 and 130 using prime factorisation method.
Answer
LCM( 92, 104, 130 ) = 11960
Explanation
Step 1: Write down factorisation of each number:
92 = 2 · 2 · 23
104 = 2 · 2 · 2 · 13
130 = 2 · 5 · 13
Step 2 : Match primes vertically:
| 92 | = | 2 | · | 2 | · | 23 | ||||||
| 104 | = | 2 | · | 2 | · | 2 | · | 13 | ||||
| 130 | = | 2 | · | 5 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 92 | = | 2 | · | 2 | · | 23 | ||||||||
| 104 | = | 2 | · | 2 | · | 2 | · | 13 | ||||||
| 130 | = | 2 | · | 5 | · | 13 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 5 | · | 13 | · | 23 | = | 11960 |
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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