Find Least Common Multiple of 6468 and 14300 using prime factorisation method.
Answer
LCM( 6468, 14300 ) = 2102100
Explanation
Step 1: Write down factorisation of each number:
6468 = 2 · 2 · 3 · 7 · 7 · 11
14300 = 2 · 2 · 5 · 5 · 11 · 13
Step 2 : Match primes vertically:
| 6468 | = | 2 | · | 2 | · | 3 | · | 7 | · | 7 | · | 11 | ||||||
| 14300 | = | 2 | · | 2 | · | 5 | · | 5 | · | 11 | · | 13 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 6468 | = | 2 | · | 2 | · | 3 | · | 7 | · | 7 | · | 11 | ||||||||
| 14300 | = | 2 | · | 2 | · | 5 | · | 5 | · | 11 | · | 13 | ||||||||
| LCM | = | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 7 | · | 7 | · | 11 | · | 13 | = | 2102100 |
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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