Find Least Common Multiple of 210000 and 396000 using prime factorisation method.
Answer
LCM( 210000, 396000 ) = 13860000
Explanation
Step 1: Write down factorisation of each number:
210000 = 2 · 2 · 2 · 2 · 3 · 5 · 5 · 5 · 5 · 7
396000 = 2 · 2 · 2 · 2 · 2 · 3 · 3 · 5 · 5 · 5 · 11
Step 2 : Match primes vertically:
| 210000 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | · | 7 | ||||||
| 396000 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 5 | · | 11 |
Step 3 : Bring down numbers in each column and multiply to get LCM:
| 210000 | = | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | · | 7 | ||||||||
| 396000 | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 5 | · | 11 | ||||||
| LCM | = | 2 | · | 2 | · | 2 | · | 2 | · | 2 | · | 3 | · | 3 | · | 5 | · | 5 | · | 5 | · | 5 | · | 7 | · | 11 | = | 13860000 |
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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