Question
Find Least Common Multiple of 1763 and 413599800 using division method..
Answer
LCM( 1763, 413599800 ) = 413599800
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1763 | 413599800 |
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 | 1763 | 413599800 |
| 1763 | 206799900 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1763 | 413599800 |
| 2 | 1763 | 206799900 |
| 2 | 1763 | 103399950 |
| 3 | 1763 | 51699975 |
| 5 | 1763 | 17233325 |
| 5 | 1763 | 3446665 |
| 17 | 1763 | 689333 |
| 23 | 1763 | 40549 |
| 41 | 1763 | 1763 |
| 43 | 43 | 43 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1763, 413599800 ) = 2 · 2 · 2 · 3 · 5 · 5 · 17 · 23 · 41 · 43 = 413599800 .
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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