Question
Find Least Common Multiple of 144, 71 and 265 using prime factorisation method.
Answer
LCM( 144, 71, 265 ) = 2709360
Explanation
Step 1: Write down factorisation of each number:
144 = 2 · 2 · 2 · 2 · 3 · 3
71 = 71
265 = 5 · 53
Step 2 : Match primes vertically:
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 71 | = | 71 | ||||||||||||||||
| 265 | = | 5 | · | 53 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| 71 | = | 71 | ||||||||||||||||||
| 265 | = | 5 | · | 53 | ||||||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 53 | · | 71 | = | 2709360 |
This solution can be visualized using a Venn diagram.
0,0
144
71
265
2
2
2
2
3
3
71
5
53
The LCM is equal to the product of all the numbers on the diagram.
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