Find Least Common Multiple of 48, 60 and 110 using prime factorisation method.
Answer
LCM( 48, 60, 110 ) = 2640
Explanation
Step 1: Write down factorisation of each number:
48 = 2 · 2 · 2 · 2 · 3
60 = 2 · 2 · 3 · 5
110 = 2 · 5 · 11
Step 2 : Match primes vertically:
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||
| 110 | = | 2 | · | 5 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 60 | = | 2 | · | 2 | · | 3 | · | 5 | ||||||||
| 110 | = | 2 | · | 5 | · | 11 | ||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 11 | = | 2640 |
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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