Question
Find Least Common Multiple of 186807600 and 1765 using division method..
Answer
LCM( 186807600, 1765 ) = 186807600
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 186807600 | 1765 |
Step 2 : Divide the given numbers by smallest prime number. In this example we can divide by 2.
(if any number is not divisible by 2, write it down unchanged)
| 2 | 186807600 | 1765 |
| 93403800 | 1765 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 186807600 | 1765 |
| 2 | 93403800 | 1765 |
| 2 | 46701900 | 1765 |
| 2 | 23350950 | 1765 |
| 3 | 11675475 | 1765 |
| 3 | 3891825 | 1765 |
| 3 | 1297275 | 1765 |
| 5 | 432425 | 1765 |
| 5 | 86485 | 353 |
| 7 | 17297 | 353 |
| 7 | 2471 | 353 |
| 353 | 353 | 353 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 186807600, 1765 ) = 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 · 5 · 7 · 7 · 353 = 186807600 .
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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