Question
Find Least Common Multiple of 11642400 and 1764 using division method..
Answer
LCM( 11642400, 1764 ) = 11642400
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 11642400 | 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 | 11642400 | 1764 |
| 5821200 | 882 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 11642400 | 1764 |
| 2 | 5821200 | 882 |
| 2 | 2910600 | 441 |
| 2 | 1455300 | 441 |
| 2 | 727650 | 441 |
| 3 | 363825 | 441 |
| 3 | 121275 | 147 |
| 3 | 40425 | 49 |
| 5 | 13475 | 49 |
| 5 | 2695 | 49 |
| 7 | 539 | 49 |
| 7 | 77 | 7 |
| 11 | 11 | 1 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 11642400, 1764 ) = 2 · 2 · 2 · 2 · 2 · 3 · 3 · 3 · 5 · 5 · 7 · 7 · 11 = 11642400 .
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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