Find Least Common Multiple of 108, 360 and 408 using prime factorisation method.
Answer
LCM( 108, 360, 408 ) = 18360
Explanation
Step 1: Write down factorisation of each number:
108 = 2 · 2 · 3 · 3 · 3
360 = 2 · 2 · 2 · 3 · 3 · 5
408 = 2 · 2 · 2 · 3 · 17
Step 2 : Match primes vertically:
| 108 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||||
| 360 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | ||||
| 408 | = | 2 | · | 2 | · | 2 | · | 3 | · | 17 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 108 | = | 2 | · | 2 | · | 3 | · | 3 | · | 3 | ||||||||
| 360 | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | ||||||
| 408 | = | 2 | · | 2 | · | 2 | · | 3 | · | 17 | ||||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 3 | · | 5 | · | 17 | = | 18360 |
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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