Question
Find Least Common Multiple of 765, 635 and 235 using division method..
Answer
LCM( 765, 635, 235 ) = 4566285
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 765 | 635 | 235 |
Step 2 : Divide the given numbers by smallest prime number. In this example we can divide by 3.
(if any number is not divisible by 3, write it down unchanged)
| 3 | 765 | 635 | 235 |
| 255 | 635 | 235 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 3 | 765 | 635 | 235 |
| 3 | 255 | 635 | 235 |
| 5 | 85 | 635 | 235 |
| 17 | 17 | 127 | 47 |
| 47 | 1 | 127 | 47 |
| 127 | 1 | 127 | 1 |
| 1 | 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 765, 635, 235 ) = 3 · 3 · 5 · 17 · 47 · 127 = 4566285 .
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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