Question
Find Least Common Multiple of 1763 and 741200460 using division method..
Answer
LCM( 1763, 741200460 ) = 741200460
Explanation
Step 1 : Write the given numbers in a horizontal line.
| 1763 | 741200460 |
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 | 741200460 |
| 1763 | 370600230 |
Step 3 : Continue dividing by prime numbers till we get 1 in all columns.
| 2 | 1763 | 741200460 |
| 2 | 1763 | 370600230 |
| 3 | 1763 | 185300115 |
| 5 | 1763 | 61766705 |
| 7 | 1763 | 12353341 |
| 7 | 1763 | 1764763 |
| 11 | 1763 | 252109 |
| 13 | 1763 | 22919 |
| 41 | 1763 | 1763 |
| 43 | 43 | 43 |
| 1 | 1 |
Step 4 : Multiply numbers in first column to get LCM.
LCM( 1763, 741200460 ) = 2 · 2 · 3 · 5 · 7 · 7 · 11 · 13 · 41 · 43 = 741200460 .
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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