Question
Find Least Common Multiple of 144, 72 and 265 using prime factorisation method.
Answer
LCM( 144, 72, 265 ) = 38160
Explanation
Step 1: Write down factorisation of each number:
144 = 2 · 2 · 2 · 2 · 3 · 3
72 = 2 · 2 · 2 · 3 · 3
265 = 5 · 53
Step 2 : Match primes vertically:
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 265 | = | 5 | · | 53 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 144 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||
| 72 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | ||||||||
| 265 | = | 5 | · | 53 | ||||||||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 53 | = | 38160 |
This solution can be visualized using a Venn diagram.
0,0
144
72
265
2
2
2
3
3
2
5
53
The LCM is equal to the product of all the numbers on the diagram.
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