Question
Find Least Common Multiple of 659736 and 1764 using division method..
Answer
LCM( 659736, 1764 ) = 659736
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 659736 | 1764 |
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 | 659736 | 1764 |
| 329868 | 882 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 659736 | 1764 |
| 2 | 329868 | 882 |
| 2 | 164934 | 441 |
| 3 | 82467 | 441 |
| 3 | 27489 | 147 |
| 7 | 9163 | 49 |
| 7 | 1309 | 7 |
| 11 | 187 | 1 |
| 17 | 17 | 1 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 659736, 1764 ) = 2 · 2 · 2 · 3 · 3 · 7 · 7 · 11 · 17 = 659736 .
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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