Question
Find Least Common Multiple of 1761 and 809735976 using division method..
Answer
LCM( 1761, 809735976 ) = 809735976
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1761 | 809735976 |
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 | 1761 | 809735976 |
| 1761 | 404867988 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1761 | 809735976 |
| 2 | 1761 | 404867988 |
| 2 | 1761 | 202433994 |
| 3 | 1761 | 101216997 |
| 3 | 587 | 33738999 |
| 7 | 587 | 11246333 |
| 7 | 587 | 1606619 |
| 17 | 587 | 229517 |
| 23 | 587 | 13501 |
| 587 | 587 | 587 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1761, 809735976 ) = 2 · 2 · 2 · 3 · 3 · 7 · 7 · 17 · 23 · 587 = 809735976 .
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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