Question
Find Least Common Multiple of 1, 48 and 85 using prime factorisation method.
Answer
LCM( 1, 48, 85 ) = 4080
Explanation
Step 1: Write down factorisation of each number:
1 = 1
48 = 2 · 2 · 2 · 2 · 3
85 = 5 · 17
Step 2 : Match primes vertically:
| 1 | = | 1 | ||||||||||||||
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||
| 85 | = | 5 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 1 | = | 1 | ||||||||||||||||
| 48 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | ||||||||
| 85 | = | 5 | · | 17 | ||||||||||||||
| LCM | = | 1 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 17 | = | 4080 |
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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